Third lectures about the non-invertible symmetries by Sakura Great, thank you Okay, is this on? Yes, all right great, so let's start with a recap of last lecture and The main gist of it was we wanted to go back to the problem of studying the symmetries in two dimensions and we started with something very trivial in the sense that we just have a Zero forms of global symmetry in two dimensions Nothing fancy. It's completely invertible. It has essentially topological lines labeled by elements of a group Let's take g to be finite. So here g is finite But doesn't have to be a billion who shall we? And it fuses according to the group law the one g the one h is the one gh and Then we said let's gauge this zero form symmetry and one way of doing that was to actually Take the following perspective and this is I'm only repeating this perspective because this is the one that will use also nine higher dimensions So we take the two-dimensional theory and we take a product with a one-dimensional topological theory and this one dimension topological theory has the same g zero The same group g appearing here Symmetry what that meant is a one-dimensional topological theory has a bunch of a cure and Now there's a group acting on these back So the group acting on the back here will basically furnish some representation of this group It'll decompose the vacuums to some erupts and we're just taking the product of these two and then gauge this diagonal g and The point was once we gauge this this product t's is to be a product It becomes actually now sort of a topological defect This is this one d t q of t becomes now a defect in this theory and this is now as before labeled by representations and So of the group gene And so now if you're asking what actually is diffusion on these guys Well, this just descends from how these one d t q of t is used these were just representations And so they will fuse according to one of these defects with representation R1 our representation R2 will be a sum over some integer coefficients here times d1 R3 and Just to be very very clear these coefficients here are nothing other than the things that you do in your group theory lectures Right you decompose the reps R1 R2 This is not here the tensor product of representations and you have a clebsch Gordon decomposition into Ereps R3 say with some coefficients and multiplicities and you know very well that this is usually not just one term But it's a bunch of irreps and so in this sense the Symmetry after we've gauged for at least a non-abelian symmetry group G becomes Non-invertible, right? I did this example when G was a billion and essentially everything is characters and this actually turns out to be a group again but if G is non-abelian this Object which are called web G is just a representations of G Is a non-invertible Symmetry in two dimensions and it's this sort of thing that will not generalize to higher dimensions Where these kind of non-invertible structures are not that? Well understood yet, and it gives us a nice systematic way of constructing such non-invertible Are there any questions about this so far? This is just sort of the recap from last week not last week, last lecture It's been a long week Some time dilation in my head. Anyway, okay, so let's we generalize this to higher dimensions and If the idea will always be you start with a theory you take a product with a TQFT So this theory has some group G zero acting Still hear me something So this is a TQFT with G Symmetry and I'll explain what this is in concrete detail and in three dimensions and Then what we're doing is we gauging G and then this becomes a measure keep this So this is a TQFT. In fact, I want it to be a dimension One and this becomes a DD minus one defect Yep So once we are in higher dimensions While the TQFT that we take the product with the should have dimension D minus one It can also be of different dimension Then you will construct different types of defects here I will start with a zero form symmetry and I'm saying okay I would like to actually construct So to speak the defects that are actually now the analogs of these lines Like the dual symmetry so to speak and so this is basically then a D minus one topological defect I want to know what are actually these types of defects but indeed in the In the paper and I now try to actually spell my collaborators last name correctly This is the correct spelling And so in this paper you'll see lots of different things you can gauge even You can even have GP P form symmetries or higher group symmetries And then you have that defect of different dimensionality that you can construct in this way Just to make sure I understand so even keeping the zero form symmetry. Can we reduce the dimension of the TQFT? So you could in principle also for example in a tool. I will do actually the case of a 3d theory 3d T And I could also take up the set of topological lines and try to construct the rep and I'll get some lines And in fact indeed I do have these rep G lines in the gauge theory They're also there. I will get to them in a moment So in fact, this is what the abstract thing in these things this is the notation these will call theta defects For the reasons I explained yesterday That's like a theta angle Yes Are you assuming that G is a non-anomalous in the DQFT? Yes, so absolutely Can I take like an anomalous? Simmer in the DQFT and in this case I get like a defect attached to Yes, I guess you could yes something some sort of a non-genuine type thing. Yes, sure So I think this is literally just the simplest way to Implement this sort of construction, but as I said also yesterday you can now go wild with this You can do all kinds of things even non topological defects. You could construct in this way Okay, well, let's get now to the three-dimensional so T is a 3d theory with G0 So G0 is generated Basics I did some topological surfaces, but anyway, this is not important So now actually what I would like to do is in this three-dimensional theory This is theory. It has this G acting on it. I now take a product with a 2d TQFT that has That has G0 symmetry and So and then proceed in the same way So the first question you need to answer is actually what such 2d TQFTs with G7 tree and Then what is their fusion and then this will tell us the theta defects and the fusion in the theory T mod G By that sort of the logical progression and so that's what will this does now and actually um Will give us the first example of a nice Such structure so these TQFTs are Also known as G SPT phases SPT for symmetry Protected topological Phases so this comes out of sort of a cotton and smatter literature really and And they're actually classified at least in okay, some of these are classified The more general dimension this can be more complicated But the ones that will be interested they're classified by group cohomology our case. This will be Omega and H2 of G0 And I explained very quickly to give you an intuition why this is Sort of an interest why this could be correct and actually if you are Someone who's worked with string or defaults. Omega really is something like discreet torsion in Or before constructions and strings here if this is helpful So one way of thinking about this is we've seen they have sort of we're starting with a G symmetric theory So we have some lines say that are actually GNH and GH type lines and we're trying to actually ask what kind of Objects could be attached here some phases Omega GH Sort of right before we're just saying there's some kind of composition of these group Elements and it's just G times H, but now when I say actually I can attach a phase here There's some Omega in you one so what are they allowed Such phases and they of course need to be consistent with things that we also looked at Like these sort of diagrams If I do G at HK GHK GHK Why it needs to consistent with these numbers of decorating these these omegas and Now you can see they'll be a non-trivial consistency condition on these omegas because they'll basically say Omega GH first Times Omega and now here. I'm coming in with GH Right, so this is like Omega GH comma K That needs to be the same as first HK and then Omega and now here we have HK and so this is GHK So this sort of identity actually says that is this is sort of saying in some sense This is the Delta Omega and this sort of Choreological sense is zero So it's in this sort of Choremology it's a U1 valued map from G to G right so Omega is a map from G to G D times G into you one point and it satisfies these conditions and that's precisely the sort of thing Okay, I There's more to this story But that's what we'll need for the for the moment. So these type of sort of trivial TQ of T's right it they really are just characterized by the fact that they have this symmetry They will be the things that we can now attach Here if you're preserving the full G symmetry So I'll now tell you what actually is sort of the set of TQ of T's that we can attach to the 2D TQ of T's Basically that two sort of sets of things we can do we can say either they preserve and then there's one vacuum and There's one vacuum basically for each choice of these For each H2 But we all know if you have a symmetry and you have such a two-dimensional Theory you can also now look at lack of an extra break symmetry So you can have a G is broken spontaneously to H the subgroup spontaneous symmetry breaking and Then also When you do that you break to a subgroup and there's a multiplicity So now they're that G mod H Many vacuar But again once we have an H we can also turn on an H SPT phase So in fact what we have is G mod H vacuar with SPT phase for H I in element in H2 and let's call it Omega H and that actually gives you all the 2D TQ of T's and so Lo and behold what we find is these 2D TQ These 2D TQ of T's are basically labeled by Some H and some alpha H and H is basically any subgroup Including the group itself any subgroup So these are the 2D TQ of T's these are the 2D G TQ of T's Then we can use to play this game of these data defense and Now the question is when we have these what is actually now their fusion and Yes, yes So when you say that there are G mod H vacuar Do you mean that the number of vacuar is the order of that quotient right or because in the previous case in one dimensions We had generic irreducible representations of G So the number of vacuers not necessarily as many as the order of the group Yes, so here the multiplicity is really given in terms of the this coset So we'll do an example. It's that that determines the multiplicity of the so you essentially Have symmetry breaking and in each vacuum you have an H symmetry, but you have G mod H many such Suppose the G is completely broken. Why can't I have a generic representation of G? Ah, but we I haven't said anything about representation yet. I haven't told you anything about Representation this is literally when the number of vacuers fixed and I can they cannot form a more generic representation Oh, you mean on top of this? Yes, because in the one-dimensional case where we had G and we said the number of vacuers is the dimension of our generic Representation of G. So you're saying each one of these things could form something more complicated. Yeah, that's my question Because here it was essentially just Everything was just determined in terms of the decomposition into representations, right? And here I think it's really a statement about in each one of these So for example, you could have asked is there also maybe a choice of different SPT phase But that actually can because actually this group G mod H so acts on these so You will find in the actual Line also in this what we're constructing here at these surfaces. There is actually a representation decomposition Secretly in this which is in the lines. So this is actually happening again on the level of the line So maybe this is or it's hidden. Okay, let me let me think about it Okay, so We're saying our TQT is a basic these on H some omega H and I would like to know what is the Refusion of To such T. So actually what I will do is I will restrict Okay, I don't know. Okay. Yes, I will restrict in this for the moment in fact completely to G abelian In fact, you can do this also more generally and I think then when yours what you're saying is completely correct You could do something more complicated But even what we'll see is in the G abelian case There is now also some non-invaluable structure So G zero abelian Okay, so G abelian so for example think about it as just a cyclic group and we'll do Z2 or Z4 these type of examples So essentially what the what the in this case? tensor now Tk Omega K right so H and K are both subgroups of G and there are these Cosycles, but potentially attached so this actually gives just some multiplicity That's T H intersected K comma Omega H intersected K So let me unpack this and explain to you what is actually this multiplicity and If this multiplicity isn't one then that also is already a non-invaluable Right because this is not a fusion that you could then easily invert or invert at all Okay, so each of these TQT's I think I can think of essentially as Right we said there's a bunch of vacuums vacuums may one the G mod H and you want to take the tensor product with K and the vacuums here are say W1 WG mod K order and So now what you'll get is in the decomposition This will essentially mean the vacuums over here are just going to be something again like the IWJ and What is actually the symmetry in these vacuums? The symmetry That's unbroken is going to be Exactly H intersected K Right, so you have in one set of vacuums H and the other K and now you'd like to know in this combined set actually what's preserved is this subgroup H mod K H intersected K So in fact, you get H intersected K And then there's a story with the co-cycle That actually goes along for the right But now the question is what is actually the small duplicity, right? So here So we get these toggle vacuums and now what we have is a symmetry that's unbroken. That's H intersected K so we start with G and In these vacuums we have an H Intersected K subgroup so now we have of course a Decomposition and H intersected K. So in fact this number here will be simply So Reduction of how many of these you had how many these you had modulo the action of this group So this number here might be decomposed now all these like you are into Orbit of this new subgroup and that's this quotient G mod H Times G mod K That's just the total number of vacuums But then we have to mod out by the group that we're now using the orbiting into and that's H intersected. Does that make sense? So this is now a non-trivial multiplicity potentially and if this is unequal to one, this is definitely a non-invertible Inclusion So our story was These are now the TQ of T's they fuse in this way Now we actually put them into our 3d theory we gauge and we should be getting something Non-invertible as a topological defect in these theories. So now we basically do the map H Omega H It becomes now defect in this case as well as a two-dimensional defect of D2 and I actually it's a little bit more convenient to label it by the coset comma omega H All right, and these are now topological surface defects this theory mod D0 right and this theory here the 3d theory This is what we get over here So I want to make an example Because you might think whoa, but now you're talking about a billion groups. Are you sure this is actually going to give something on invertible and it does So are there any questions about the general sort of story? So it is important that the co-cycle is non-trivial like I think when the co-cycle is non-trivial it's projected representations So in fact if I were to do the Z2 times Z2 example, which is the first that has actually a non-trivial co-cycle This whole thing becomes a very very complicated category and you can look it up in the appendix of those paper and It's a very rich structure already And I'll restrict myself to Z2, but you already see in Z2. This is quite interesting Okay, thanks, but you're right with the co-cycle. There are more choices you get more defects And you need to also then track that this I didn't tell you what this is But there's a little bit of a story how you actually construct this co-cycle From the ones you have over there Okay, but let's you know First look at the simplest example at any other questions Prepare this example. So what are the subgroups of Z2? Okay, and this will sound very trivial because it's not particularly So there's the trivial subgroup. Let's call it one so this trivial subgroup and then It's a simple group So there is Z2 so these are the two subgroups and In the in this case H2 of Z2 U1 Is actually 0 and This is common. I just made a Christian is basically if you want a Non-trivial co-cycle if you want omega non-zero Look at the Z2 Because I'm too short for this Okay So this is a reason of the starting point when we have a relatively simple setup Now what we have is essentially so this is the case what is symmetry? So my age is sort of fully preserved G is fully preserved and this is why it's completely broken So let's look at the case H is equal to 1 So in this case actually Okay, so this is like one vacuum and G is unbroken and I want to call this vacuum zero and Let's call this defect Accordingly D to it. It is right. So this is So this is basically G mod H is like one So H is equal to 1 So the tool is completely broken But it is symmetry breaking completely to nothing. So in this case what we have is and the two vacuums And then so the gene mod H is two and I want to call them plus and minus And now what we have to do is Okay in the defect Associated to this. I want to call D to Right, so H. This is just that G mod H is now Z to now We would like to calculate the fusion of these two defects. So D to it With itself That's one vacuum on one vacuum. They're unbroken subgroup as the intersection of Z to with itself at Z to D to it With Right, so now we have here. This is one vacuum. We have here the two plus minus vacuums So We have here H is Z to and here H is trivial So the intersection of these is trivial. So this is gonna be D to Z to right because in this case H intersected K is just again trivial The question is what's the multiplicity? So we get two vacuums, right zero tensor with zero tensor one a plus plus zero minus but the Group act is one orbit. So we get just one And now we also have So far these look completely boring These fusions, right? There's a whole list super super nice and very Invertible looking and now the question is what is D to Z to with D to Z to remember This is the one right where H is equal to trivial K is equal to one. So I actually age intersected K is gonna be one as well So we get D to Z to But now we have got here say plus minus and also plus minus And now what we get here is if you decompose into these orbits we get plus plus minus minus Plus plus minus plus minus plus in terms of the vacua and now of course the Z to the two orbits of These I can also just stick it in this formula when this is to get two orbits and They are telling us there's a two. So this is our first truly devised non-invertible fusion and non-two-dimensional theory So some of you will notice and will say well, I've seen this before And actually this is not a coincidence, but let me just pause for question at this point about this example so very Quick question So the fusion rules you wrote are all abelian in a sense Does this depend on the group being abelian or it's Does this depend on the group being abelian or it's just a structure that is from, you know Yeah, so here these are all abelian things but For could I mention one defect that can't be non abelian this type of you know What I'll call triality defects condensation but here these are all appealing because everything is just determined in terms of the vacua So abelian in the sense of the the order doesn't matter. I mean here the order doesn't matter anyway, but okay Do you have a question? Yeah Forget for the technical question, but is this the higher gauging on the one? Exactly, so Francesco was just saying is this the higher gauging indeed these are exactly the condensation defects so These are the two two are also Constructible by Gaging a higher form symmetry a one-form symmetry in this case a one-form symmetry on a subspace In a two-dimensional subspace This is working. So this is what's called condensation defects And that's sort of what's been discussed in this paper here and introduce them and I want to explain a little bit how that all fits together So we started with a theory that had a zero-form symmetry We gauged it and then we get these topological defects now What actually we have is a little bit more than that so we started with a 3d theory t with G0 is equal to Z2 and Then someone should have at that point said to me wow hold on you told us in the first lecture It's a B at the end. There's a dual symmetry. So in T mod G0 we have The dual symmetry at the dual to a zero-form symmetry in three dimensions is a one-form symmetry So we have a dual as well, right? So this is Z2 one form and Z2 is Z2 one form is generated by topological lines D1G Okay, well D1 minus. Let's call it with D1 minus with itself Is the identity? I just align topological lines that generate a one-form symmetry at Z2 So if you now I should take stock. So what what is actually? What is the full symmetry of this theory T mod Z2 I want to do this over here. This is now a collection of different things, right? We reconstructed these D2 Z2 this these surfaces. We also have these topological lines and so this whole thing comprises the full collection of objects that We should call a symmetry. So this T mod Z2 zero has It has surfaces It has surfaces. It also has lines. This is completely invertible, right? This is this is just group like but these here have these non-invertible fusion And now the question is and then also secretly you have points You could think of like points like things on these lines, but actually not that interesting in this case so what you actually have is This collection of things and this is not new because in two dimensions We really had only lines and junctions points. Now we have surfaces lines and then this point. This is actually the full structure. So mathematically Okay, so let me answer two things. The first question is how does this fit with this sort of statement and the statement is these surfaces so in fact these D2 Z2 We can think of as we take the trivial surface and we gauge The Z2 one form, right? So these are the lines with the one-form symmetry These are the zero-form on On it. And this is also known as the condensation surface on some M2 for the V2 one So this is the connection between condensation surfaces and these data defects So these data defects give you the condensation surfaces for the dual one-form symmetry The data defects are the condensation for the dual one-form symmetry That's the first comment the other comment is Now if you are a mathematician and you know in all of these we have fusions, right? In addition, you have all of these as a fusion structure So some composition of these topological defects and what this structure actually is is Is something that people would call a two Fusion Category and so the two refers to the fact that we don't just have one layer of lines and then some points the points are like You know Things that sit between two lines. We actually have surfaces between two surfaces There can be lines and between two lines that can be points. So it's this sort of three-layered structure So we have surfaces and these are what they would call objects in your category These are morphisms or one morphisms and these are two morphisms But really this is just in some way that you could for the moment and think of it as terminology because and All it describes is what we just derived in terms of a physics picture and So I write one picture that's made useful is so you can think of you have these D2 for example D2 Z2 And then you can have topological lines Actually, let's not specify what so you have some kind of objects Let's leave it by a you can have two of these and then there's a lot a topological line here D1 AB D1 a a B prime and then here it is a D0 That is a junction between these two topological lines. I think maybe this is the moment that the color is coming in handy these here You have a line here and Okay, so that in particular This specific thing we construct that is in particular When you start with a three-dimensional theory T with G0 Remember in two dimensions. I just said is let's call this your back G It's vector spaces graded by G. These are just topological lines labeled by G with G group fusion so in three dimensions in analogy These are actually these D2 G surfaces right that we started with that were completely invertible and Their lines and there are actually the lines one G and points They form also now a two-category and this is the two-category two back G might start G back G and one dimension into two dimensions V dimension to a two-back G Now when we gauge this and not surprisingly we get the team on G theory and Here we have these D2 Z2 D2 it and V1 it V1 minus and then some points This object here is called to Rep Indeed you see that in fact this the lines here form exactly the representation the one rep And so if this one on a bill and you would also get non a billion lines here And that's exactly how you would see that there's more to this So this is just the label for what you just constructed Okay Okay, this practice this data defects coincide with the condensation defector is the most general situation I mean in in generic dimension Is it not true? so I will Do an example probably this afternoon where there's stocking with TQFTs We'll give you another condensation Okay, I see that you can get the old condensation defects Plus stacking of the couple to give these Because so here we are in two diamond the 2dT QFTs here you get this is what you get And this is you can always think of it as compensation But when we actually don't go to four dimensions, which is obviously interesting for various reasons You can stack with 3dT QFTs now when you have 3dT QFTs you can have non trivial topological order So it's not just labeled by not they are well basically a bunch of accurate and some representation theory on these Compositions, but you can have genuinely not interesting 3dT QFTs with g symmetry that you can attach and gauge And in that way, and I'll do it example. So for example If you have a mixed anomaly, you cannot even just stack something that is sort of trivial like these So 3dT QFTs, which is labeled by Cosycles you actually need to stack something to cancel anomaly So that's actually you want to Simon's theory for example in three dimensions and then the associate defects are not Actually in the different frame the duality defects It's still true that in the TQFT that you put the GCM that you must be non anomalous in the full Well, it must be non anomalous in the sense if the theory you start with is non anomalous Then yes, but in the case right when you have a anomalous Transformation the theory before you gauge I will do this example You will see that you actually need to cancel the anomaly first and then you use it the 3dT QFT to Stack it on top canceling anomaly, so then you can gauge the bike is working like an inflow for that Okay, but that's going ahead When we gauge our discrete symmetries usually we get also the magnetic symmetry on top of the electric one Which is in the lines that you constructed You mean this there's the dual symmetry There is the dual symmetry and also the magnetic one usually like if I gauge a Z2 symmetry I get two two Z2s after the gauging one is Generated by the Wilson lines And the other by the yeah, but then they are they are not genuine, right? Yes, I mean they have stuff attached So I really here I'm talking about symmetry generators. They're topological defects that are genuine For example if I gauge a Z2 symmetry in a trivial theory I get a Z2 gauge theory, which has two two symmetries one Z2 electric and Z2 magnetic Then okay, if I add matter maybe some some symmetry can be broken but generically I think Yes Okay, but do you agree that in this case when it start with a zero-form symmetry, right? Maybe the way I can answer this question is to write down the Right there's in this theory. There's a about 40 Tqft the same tft that has About 40 theory that has basically be to delta C1 And all I'm doing is I'm imposing different boundary conditions on that So I'm there is no room for an extra Z2, right? I mean, I started with something that was generated by flat But by C1 so C1 was the map background for the zero-form and then I actually Changed the boundary condition to be to being the background. That's the one Maybe we can discuss Okay, so this was a very abstract Analysis, I want to tell you an example of actual 3d quantum field theories where these gadgets are appearing in real life They're not complicated theories at all In fact, they're surprising So what are actually examples? 3d Qfts with such tool that tool or tool that G Generally symmetry For Z2 which equals to Z2 You can start with the zero-form symmetry and in fact The if I have gauge groups, so I just take pure G gauge Is equal to SO3? and I'll go to G gauge is equal to SU2 Yeah, mills It's not that this is the most interesting three-dimensional theory to look at but it gives you an idea of what actually The title series are where you would see these things and then four dimensions. They'll be interesting actually Series So the pure gauge theories this one has a Z2 zero-form symmetry So this is that has a two-back Symmetry and when I gauge I get a V2 one and all these conversation defect also, and this is the two-rep V2 Right in one way of seeing this is this SU2 has a one-form symmetry It's just a center. This is just a center symmetry and From the center symmetry. I know these I can construct either by conversation Or I can think of them as coming from the SO3 Where this one form actually becomes zero-form in three dimensions? But it's just the the analog of the magnetic one-form symmetry 40 where there was a one-form symmetry here It's a zero-form symmetry the dual and I can take that gauge it and then these are the theta defects I think and think of these as the condensation defects or theta defects and of course you can extend this to other things so in for example and more complicated examples which have also Symmetries that are a little bit more interesting. So for n equals to if you do a SU n You have a Vn One-form symmetry and so actually what the full category is is actually two-rep This is the symmetry and so now you have these these Defects here we construct the Z2, but you can repeat this for Zn And then you get again non-invertible defects for that It's also an example if you have actually n equals to 3 so SU3 It's a bit more interesting because in this case there's more structure because you also have Not just this but you also have a Z2 outer automorphism Zero-form symmetry you can combine this and then you can get actually something like that So that's a more common that has topological lines that actually are forming representation of S3 So these are examples of QFTs that actually Have these sort of condensation or theta defects as symmetries but That's just one class of these type of things and actually it's it's interesting to ask are they actually also and Non-invertible symmetries and in QFTs that are not of this time not of this compensation time When do I actually have to finish? 20 million So do you have questions about these 3d examples? Because I will now discuss in a bit more detail an example that isn't quite of this type where you get Non-invertible symmetries more from this sort of perspective of The gauging of the auto-automotive I'm thinking Okay, I will discuss this example that may actually fit in better and then I'll do this other thing later So in fact, let's continue along this this line of reasoning. So we had these theta defects And so now actually it goes to D goes to 4 Right, so you do care about what I mentioned quantum field theories and now What we can do here is Why the mantra was take this and now stack it with a 3d GT QFT or What is hearing? Engaged and that we can perfectly well do the issue is just so 3d QFTs More complicated So there's still they exist though These are analogs of SPT phases For so G SPT and again sort of in omega now in H Me G You want But they're also that genuinely non-trivial 3d QFT and so these are going to name a 3d topological order a Lot of coins matter theory is about understanding these better Measuring them in the lab. And so then they characterized by categories themselves and these are the so-called modular pencil category So in principle when we do this data defect construction, we are not limited to taking just these type of SPT phase QFTs that we could also be stacking something more non-trivial and in fact sometimes with with TQFTs That even non topological Boundary so if this is obscure I'll explain them on what this is on top of logical boundary conditions so for example Transiment theory for some group G with some level K and the boundary if I put them on some space M3 Where the boundary of M3 is sigma 2? We all know that this gives actually a carl CFT. That's a CFT 2 WDW at level K for example So sometimes you actually even need to do this and so there's obviously something non-trivial living even on these Boundaries of such theories and that's very different from these type of SPTs. They are relatively trivial And I'll give you an example. That's an interesting physics example that also illustrates That there's a much richer structure in terms of what we can use in terms of constructing theta defects What we call twisted theta defects because these are they would call these things This will give rise to theta defects organization and All of this here if you stack with that Call twisted theta defects and it's the same principle We take the TQFT we gauge the G and then the TQFT becomes a defect and the gauge theory And so actually most constructions of non invertibles actually That arise from some sort of gauging Fit into this framework. That's why it's nice to organize it in this way While then sort of discuss different constructions successively using different tools So the example I want to discuss is Is one that was first discussed by Heidi one of the two first papers We can also this was this other paper the duality defect paper But this construction here ties in exactly to these types of stockings with TQFT and it's and I apply it to 40 And it goes to one super young males say with SU2 gauge group or gauge algebra That's a theory we should all care about Because it has right so it's known that the SU2 group theory that actually has a into this confinement in the IR and very interesting vacuum structure So What actually characterizes this theory? I'm actually let's start with the the group as you to This theory is it's super symmetric That's only relevant for the following fact. So 40 and it goes to one super symmetry implies that you have a U1R symmetry But this in this case gets broken I'm too bi-normally to the Z to N Zero-form symmetry. So this is a zero-form symmetry in this theory And it also has a center. So actually doing it for N So let's refresh your end It has also a one-form symmetry That's actually quite crucial for the confinement Which is the N these two symmetries of global symmetries Those are the gauge symmetry but we don't worry about that too much and these have also mixed anomaly. So when we have a One-form symmetry that the background field B2 a zero-form symmetry There's a background field a one and this makes anomaly. We'll have the following one five E2 squared All right, so this lives in some five-dimensional space or the four-dimensionally. I'm not very on this boundary So this is the anomaly and What we want to do is the goal is gauge the one-form symmetry and go to the PSU N theory and The question is what is the symmetry of that PSU N theory? Just as a quick recap for the for the SUN this one-form symmetry Will persist With this mixed anomaly to the IR and I will confine and we'll have N vacuar right so the Z to N will break to basically Z2 and then there are N vacuar and They're all confining and the question is what actually happens when you go to PSU N so The first observation is if you gauge this It shouldn't be a problem to gauge the one-form symmetry because it's not that it's a one-form symmetry only anomaly It's a mixed anomaly But there is a problem with this particular setup because if you look at the zero-form symmetry generator This is some topological quarter mention one defect Let's say one the generator for this one on some three manifold If we actually do background gauge transformation in this background gauge fields And you shift this a one actually this picks up so background gauge Transformations then what happens is actually because a one goes to Delta lambda this however is not trivial. This actually picks up a particular term. So this goes to D3 With an extra phase it's just minus 2 pi i over N B2 square And now M. This is over an M4 and this is sort of M3 With an M4 attached and that's not good Well, you can't just gauge this symmetry So there's from the perspective of the zero-form symmetry generator. There is some anomaly. There's some anomalous background gauge transformation so When you actually now gauge the one-form symmetry, this will not be a healthy defect anymore. So what we need to do is before we gauge We actually need to cure this transformation there's an almost transformation of this defect and Well, we just learned we can before we gauge stack TQFT's and so now the question is can we can cure this? stacking a 3D TQFT such that cancels the same property it has a one-form symmetry and An anomaly which is basically this 2 pi over N These two squared anomaly might have told you there are in three dimensions for the one-form symmetry that is B2 square An anomaly so I can stack something that has precisely these properties a 3D TQFT on top and then gauge because then this Variation just will cancel out and In fact in a very nice paper sin lam Cyberg Essentially in 2018 classified. What are the minimal TQFT's in three dimensions that have a certain one-form symmetry anomaly and a certain at one-form symmetry and a certain anomaly so they classified the minimal 3D TQFT's with one-form symmetry and And a given anomaly one-form symmetry ZN say an anomaly P So P times B2 squared and they call them APN and all purposes We just need a N comma once So they're called a N comma P So for N ZN one-form symmetry and P is Anomaly that you have and so what we need is we need For this defect that generates this one for a zero-form symmetry. We need the an comma one And in fact they also showed Diffusion of these might be also always need the fusion of these TQT's these fusions are actually very simple When N is fine Please don't ask me what it is for N not right Let's stick to any goes to two All purposes is a prime number and now we can ask for SU2 What actually do we get now? So we take the defect D3 one and We just replace it With a defect. Let's call it curly D3 one on the same three manifold, which is just D3 one Times this a 2 comma one For SUN you would stack it with a SUN one and This object now Has precisely and I should have said Here there is a minor so it should have precisely the opposite anomaly This actually cancels precisely this anomaly. So this has No anomalous transformation and now we're ready To gauge Now we stack this with the TQT and now we know from our general sort of understanding Well, this should now become a topological defect in the gauge theory. So when you gauge the ZN1 Z21 form symmetry What we get is now a new defect. This is now one defect in the new theory and So the D3 one Three is now a zero form Symmetry defect and the question is what is its fusion and Because we have diffusion of these guys Right now we have two of these we get exactly that here. We can actually rewrite this diffusion is actually So I can actually write it on for the N case if you want If your N is prime, maybe you would like to form it D3 1 and D3 2 and there's another fusion. So now here you see this year is a TQFT That appears as a coefficient in this fusion and then there's the fusion of the defect with its so when we stack with sort of A dagger Dagger and this actually turns out to be the condensation defect on M3 of the dual one Condensation Okay, so we get in the PSUN or the SO3 for the N equals to case these zero form symmetry generators and have these non-invertable fusions so the Generally the PSUN pure And it goes to one Superannual theory and 40 has Sort of non condensation. So these are right. These are twisted data. They are really these TQFTs, right? These are oh, okay No one asked me.  This is actually very simple in this case. It's just you want to lend char time of theory So that's why you can then do all these calculations and determine it So here we actually have a theory that precisely fits into this framework We have a char time in theory and it's boundary is not a gap theory. It's actually a two-dimensional Carol boson I'm finishing in two minutes It has non invertible Symmetry Which is basically either coming from this perspective of this anomaly and these are basically what you could call these twisted Data right the non invertibility again comes from the fact that We had to attach or we were attaching these 3d TQFTs to this zero form symmetry generator and then gauged So this is sort of the theme that goes through out all these constructions that there is some sort of a non invertibility that comes Because of them The structure of these TQFTs that fuse in this peculiar Okay, I don't any questions one minute for questions. Yep This is not the example that I was referring to But if I'm understanding correctly this construction of a twisted data defect is not really as the data defect I mean you just put a TQFT and you gauge here you are taking a TQFT, which is anomalous So if you gauge you have to attack an SPT But you are using another defect of the theory which has an SPT attached and you are fusing together Sometimes you can't gauge without actually attaching a TQFT that has some anomalous Variation right because here. This was really the key thing Yeah, okay It's the same thing because you got you're attaching the other defect the other zero form symmetry of the theory which also have a An inflow of touch and they cancel together. That's right. So here It's not an option. I mean it's not an option either Here basically this forces you before you gauge to actually attach This TQFT so that you then get a consistent Zero form symmetry generator for that so But it still follows sort of in it's there are also examples, of course you can write down things like, you know, just So simplified versions of three rap Z2 for example, and that there you would just attach SPT's But the point is when you go to four dimensions There are more TQFT's and in fact you can even if it's not anomalous You can also actually attach a 3d say an MTC with a Z2 symmetry for example, and then gauge So this category three rep G is much much richer than what you would get from just looking at these things and Indeed sometimes in physical situations you can have sort of additional peculiar things that you have to attach TQFT's Which don't have these gap boundary conditions Sorry events are also another question even in the case in which the TQFT is non anomalous You can also have a situation in which Let's do an example for example you one level k times n square if k and n are not prime You can gauge the subgroup Zn In this case, do you get a condensation defect or not? You won't have a k n square Okay, this is your theory No, this is the TQFT that I want to attach In a in a 4d theory, which has a Zn1 from symmetry because in this case I mean if you if you take this theory This is not a pure gauge theory But and there is a non-trivial extension of the n times k n Zk n, so I'm not sure whether you get if you if you if you do the data construction for the end if you get you have a 4d theory where you have a Z you were saying Z2 at Zn1 from symmetry And you want to use the subgroup Zn It's not anomalous, okay, and you want to group use the subgroup Zn of Zk n square of the TQFT through the data construction But this here is Not a just an SPT phase right? No, it's not an SPT. So it's more. It's a definitely a twisted data construction. Okay Because this will have an anomaly of the type a k n square comma 1. Yeah, but the subgroup I'm gauging is not anomalous. That's true. Yes Okay, you're saying you're sort of doing Twisted slash So a hybrid thing. Yeah Okay. Yeah, that's interesting. I have There are many different variations of this and I don't think that has been explored yet, but it's an interesting case I have a question Which is somehow I'm follow up on this. Um, so when we discussed two and three dimensions The logic in this theta defect was so we gauge the symmetry and now we classify all the TQFTs that are the given symmetry But now in this example you're saying Now in three dimensions there are non trivial TQFTs So if I try to classify TQFTs with a given symmetry there's an infinite number So it looks like I can construct an infinite number of theta defects in a given way So there's still always this construction And then there's a question and I do actually have So you need to throw a TQFT that has a g symmetry, right? It's not just any I don't want to just attach anything it should still It can of course always attach a theory that has no g symmetry and then it's just a product it stays a product but I would like to have say um Some MTC with some g symmetry so it has some z2 symmetry thing So the question is then how many are there and when I touched and what do I actually get? Well, yes, because even with this condition there is an infinite number of TQFTs with g symmetry So it looks like I can generate in a given theory an infinite number of theta defects But are they really there? There is an infinite number of symmetry Yes, no the first question is indeed what actually so there's no question that you can't do this construction So then the question is when you have such a theory and you do attach this and you gauge And you have now all these different topological effects What actually do they do in the gauge theory? Like how do they act on the act of physical degrees of freedom and how is it actually distinguished? These different sort of you know if I attach one MTC or another one How are these these symmetries so but it indeed in 4d this this category becomes extremely huge um I think here there's also a maybe a comment in the similar sort of vein I actually write this The the main point of this paper was to classify the minimal such 3d TQFTs Of course, what all this is saying is These NP comma one They're basically minimum in the sense that if you have a TQFT with this one form symmetry and that anomaly Then you can always factor it into this Times something else some other a prime That doesn't have the anomaly so here even you could say you're attaching An arbitrary sort of TQFT now. This doesn't really talk to anything in this theory So it's completely decoupled right But in principle that also you could say well, why did you use the minimal one? Actually Pavel has a comment I was just going to look for Pavel because he was in fact saying it's sometimes easier to actually Also related to this restriction here to attach All of you know, actually you probably want to have a comment about Yes, he has a question and he's he's got this construction of these q mod z Symmetries where you actually take all a billion TQFTs and then you can compute all these fusions So we've been a closed right Yeah, first kind of a comment is not quite clear how this fact ran out is canonical of this Non-normal spot is second. Yeah in principle like yeah my comment is that if when you start fusing fusing them You will go out of the of the of the class or just minimal TQFTs Yes, so this is indeed that's why here I was saying Let's restrict the prime Then you really just you can write down the action for this you want level entrant simons and just integrate out some diagonal field And then you see this fusion In fact, if you just want to look at these an comma p's and do this More generically than actually you you see that there's some issue and Pavel has written this very nice paper on this q mod z But I still don't know what actually is now the the resolution should be now Attach all a billion TQFTs So you need to speak on the microphone. Otherwise, I can't hear you. I know I else can hear so the thing is that The the symmetry g no As to act faithfully, I mean it cannot If you which symmetry the g zero from symmetry, no If you put any tqft will not act faithfully on the full tqft, you know, we will leave some operators in variant No, the the the idea of amp is the same is that you mean here? Okay Because here this this is not zero from tonight. This is a one from some Yeah, exactly then some lines are invariant and Yeah, so there's a fine this factor So first point is that Pavel is saying this decomposition is not actually canonical And if you do this you go out of this class For generic But you can work in the equivalence class that that's a well-defined object So it's a It's called the with with class So you can you can work there and then it's well defined And I think the point I mean this is how we understand it is that If you kind of factor out or you choose a representative in which the symmetry acts faithfully like in in this case It's separating amp. I don't know what is in general the way in which you choose that nice representative Then you can do everything and Added data about the the couple thing is undetectable from the bulk. So it's not physical. I mean, I don't know to Measure it, no That's true, but Yeah, what okay, so Actually, this is maybe the right moment to make the following comment So I think this came this came up yesterday And when I think chris was asking me so when did this all happen? So this all of these developments basically um, but the solar star with this paper mentioned yesterday by this small plant people then this and in the in 2021 In the fall this paper and also the gordova omore choy lamb sin paper came out And so this is a very very young field and so some of these questions are not yet as There are loads of examples And one goal is to actually understand them in a slightly more systematic way, right? And one of these questions is so can you actually put them into sort of one story that we have a description that sort of gives you Mathematically, but also sort of on a more conceptual way a description of all these non-invertible symmetries And it's clear. We don't have that yet in higher dimensions. And one reason is that these These what we get here are three categories three fusion categories. They're very very complicated objects We don't really know the full structure of them but Exactly these sort of questions Right. Well at some point, hopefully tell us what are the things that we really should be Sort of, you know, taking into account what is physically relevant, right? Like what you're saying this with class We shouldn't be looking at each defect, but maybe some equivalence class of these things But that's all really part of everyday research at this moment But I think this was not clear to everybody. That's why I wanted to at some point say it now. It seemed a good moment I think now we're really over time. No And now we are already in the discussion session. Okay Okay, but then I think people should also ask


Hi everyone, Joe for jazby's case breaks.com. We did it. Thank you very much. Nice little late-night rally We went over a little bit, but we all dug deep and we made this happen. I appreciate it We said that if we sold out that contenders break the impeccable plus the two fillers and the mystery crate plus two fillers That we would give away some money and we did it So we did that Salo pack two five six and two five seven the two fillers for the mystery crate They're the mystery crate names right there. It's actually make this a little bit bigger So there's everyone's names there There's that break there that break there and we knocked out the contenders break And then there was a lull in the action, but but late at night We we knocked out one of the filler packs for impeccable then another filler pack for impeccable And then we finally did that impeccable basketball break. So big. Thanks everybody for making it happen Now let's copy all of your names new dice new list And I think let's put back here. I think there was 195 total names on the list. So thanks everyone for making it happen. So we should see 195 items on this list as well. And there it is top Top name will win $500 a break credit Spot two through five will in a hundred bucks each. That's not too bad either. I'll send that right after this video Let's roll it randomize it. Wow snake eyes. Good luck One and Two easy All right, so thanks everybody here for making this happen Appreciate it. Congrats the top five. You're gonna win money drum roll drum roll drum roll All right, Stephen P. Very close, but not quite next five though $100 break credit going your way Oliver Jesse Kevin or next four that is and Steve Birch Name on top $500 a break credit Anthony. There you go. There you have it and That's the way it is Anthony 500 bucks going your way Steve Kevin Jesse and Oliver hundred dollars break credit going your way Thanks, everybody. Great night. Great close to the Thursday Great close to my week join Jason on Friday and Saturday, and I'll be back on Sunday Just have a nice week on YouTube jasky's case rate comm. I'm Joe. I'll see you next time for the next one. Bye. Bye You


We are live so hello Cynthia. Hello Cynthia loves global predictions. He does We do we get a chance to Get into the nitty-gritty to a certain degree As much as we possibly can That's right. Yeah Good Yeah, we got our cards ready we have We do Interesting the card on the bottom Got the eight of wands Interesting Is that up? Well, it's fast-paced changes. Oh, yeah Yeah So is that a harbinger of what we can expect? Tonight I don't know I don't know. Yeah Carrie Lake's trial is tomorrow She is going after You know her state, you know when she should have won basically Yeah Well, she's in court tomorrow because they weren't checking the signatures properly You can see clearly and she's got a few other Issues as well and it's all going through so they could have dismissed it but they didn't they've actually said yes Be careful what you say on this because you know, we can't say that the FR I Okay, I know just want to say no, it's good job. You do. Yeah Yeah Just pulled another card the tower Well, yeah, I mean the 16th is Is the tower as well 16th, so I'm getting a knife My back Why is the 16th the tower after that I got the Sun so Well, yeah, so disruption the tower is number 16 in the tower Oh, I thought you meant the 16th as in today Yesterday was yesterday. Well, it was for you. It's today, but for me it was yesterday So, you know, that's all linked, isn't it the 16th the 16th card is the tower. That's all Yeah disruption and things But we got the Sun Is that report that's just come out the dark Durham? No Report the Durham Durham report. Yes, that exposed everything Can't explain to me a little bit because obviously I've seen a little bit, but um, I'm yeah, I'm a little bit Well, it was all you know the Durham report was that basically proved that there was no Russian collusion that all those 50 Some odd FBI agents lied Hillary lied Obama lied Biden Clinton the whole Kitten Kaboodle they all knowingly lied That's the key part knowingly. That's treason and Penalty for treason is Yeah So They're probably not going to do that. Are they? Do you think if mr.  We'll just put it that way Finality Yes, I believe so. Yeah. Yeah. What do you guys think?  What should be?  Look at all, you know Epstein's list All of his clients lists You know Where are where's the justice for the children?  Mm-hmm. Yep Yep It's like we're not seeing we need to see these arrest now I mean now it's kind of like come to the light in the mainstream media It has to now something has to be done But all the time Mr. B is in charge. He's not gonna allow that to happen. He'll pardon them all boning Right, but it's absolutely obvious that the who these the FBI is working for He won't Biden won't be able to pardon anyone if they prove that there was collusion and the whole electoral process Yep, and then it was unfairly swayed Because of false information that is just coming out in the term report. So this might cancel everything Which would put Trump in office? Yeah, just like I said, I think he's gonna be I think he's gonna be in office by the first week of September Well, yeah, I agree. Um, this um, this Carrie Lake one if that goes through then She's put directly in place of this other lady if she wins this court case Well, isn't that like in order so if Carrie can do it and that's getting people think about the White Hat operation So if if everybody sees that Carrie then gets her justice It's not going to be such a big shock when they find out that mr. B's done it to mr. T And then mr. T gets put in place Can you see what I mean? It might be the step-by-step kind of like drip feeding getting people I've been shuffling the deck and look what's what's on the bottom again Eight of wands again Eight of wands the tower the Sun and the eight of wands Yeah Okay Yep Yep, and we read some of these comments guys. So if you do have any questions make sure you put them in capitals If I've got the right I haven't got the right banner at the bottom. Have I love? So hello Hello Martell See Yeah Barbara also got a question. We can go back to LA love a girl. Hello Stop and stare 52. Hello Please lot Cynthia, hey Cynthia Claudette Joanne So Martels is I think some are already and yes more will happen because it just has to happen this way Yeah, you see mr. T has tried to do everything You know with law under the law under the the the system if you like It's Hello Wow Linda we are so Linda is multitasking Canadian Truth and Freedom broadcast Okay Rose this is interesting. This is a great question. Goodness Sorry, just like JFK being offered by the three-letter agency. No one is upset not even the Irish the statues of him there Okay, so we go. I can't find it now Oh, here it is Flag over the whips at White House is upside down and I looked up why According to the US flag code flying the American flag upside down is only meant to be done as a signal of dire distress in Instances of extreme danger to life or property Whoa That coincides with the 13th of April when they and that Alexa changed the the thing to who is the president now as Of the 13th of April blah blah blah. Yes, that goes with that. That's change Everything's changed Wow Oh here it is, okay So, yeah, this is that rose Oh Go like we get that off there and go like this and Yeah, you can see the flag Upside down only meant to be done as a signal of distress In instances of extreme danger to life and property And here's a different picture from a different angle showing that it's not just one picture From one angle.  Okay, I'm just not sure specifically but It's such a big question So it's hard to for me to understand with my limited half Half a brand cell. Well, no, you're Libra. So everything's got to be Yeah Fair and orderly we can do that Surprise general. Hello. Yeah, it's um, I'm somebody bring it on. Yeah Yes People are getting ready. I think even the normies can see they think is there is that it's right out there truth bomb truth bomb truth bomb truth bomb They've all started or even the mainstream media have started turning their back on throwing mr. B under the bus they have they've started doing that and with the Flag being flown upside down at half-mast right after the Derm report Basically uncovered everything and now we got Hunter Biden's laptop being exposed as well Yeah It wouldn't surprise me if we start seeing some Some people getting taken out of the White House and as a matter of fact wouldn't surprise me if we started seeing some children Getting taken out of there too with the underground tunnels This for entertainment purposes only well because they're digging the digging it up No, because of the mass arrests that are going to be going on and then they'll be able to Finally go in and check out some of those tunnels and you know bring some of the kids out that have been down there We've already we've seen footage of them doing it already But obviously they might you know, there's now gonna be more I mean, let's face it when when mr. T was in there He cleared it out, you know when he was on on watch, you know, but um And obviously mr. B would have re-opened that wouldn't he? Yes. Hi Brian Brian Chapman. Hello and Greg. Hi All great. Thank you for joining patreon as well. I just want to say thank you So loving these questions guys. Thank you for for bringing in more questions Good Yeah, good. Yeah, I Think seeker disappeared. He didn't hear He didn't hear my Question about his initial question Can you be more specific if you're still there seeker, I don't know if you just ask a question and ran I don't know But I Think it's like the energies of mother earth. I think that's that's how I would take that It's the the energies of of her it's like well sometimes a question resonates more with you than it does with me So, yeah, you know if you want to answer that you you answer it because I I'm not I have no idea what it could be a million different things and it's just so vague No Yeah All right, so all of them all seeker's back. I just want to know if she is in 5d yet Some people it might be because some people are saying that mother earth has actually transitioned. I heard this Yeah Right. Okay. I'm ready ready ready Okay, well We can we can look into that. I'll I'll look I'll look into that now that I have a better idea of what Yeah, the question the question is and Did they say that it's gone into into 5d Has Has mother earth Entered 5d yet the cards I have I got heartbreak and sorrow and grief And I'm trying to and that goes with difficult decisions to be made and What I'm getting is not Not yet About to it's because the card after that was the Sun You know and that is you know, you know the the the dancing in the new earth right there but No, I don't I don't I'm not feeling like it's It's there yet It's in the process of being created and there may already be people that have transitioned like Dolores cannon Terrence McKenna John major Jenkins Jose Argueas, you know people who are no longer here with us. They're they're probably there helping to build it for us But it's not not yet Not yet You'll know we will we will all know and that's when the Sun card comes out and what I mean by the Sun This is the solar flash We'll know when that happens That's what I have not yet, but the solar flash it's on its way. Yes indeed Sorry, I was still trying to look for my dice Which have So anyway, I got I got the same thing money enough and we got the Two of wands, which is preparation So there's a lot of preparation going on with with Mother Earth at the moment There is the breaking free of the shackles Okay, so there has been or will be a big time release. Okay, so here this is a change Okay, the chains are coming.  You're hearing that that is the trap. That is how she's doing it Okay, there's a sound vibration going on She's she's healing at the moment From everything that's going on.  She's pleading with everybody to keep their light high To keep positive thinking to keep going forward. Okay. I do feel feel as if you know, you know We've got the world card, which is, you know, the mother earth isn't it the world? and so everything will be going into Into place very soon We have the preparation and planning so I'm picking up not quite there, but definitely on on the way so Yes, that's how I got it. I'm gonna try and look for my My dice, so I'm gonna go off camera just to look for my dice. Okay. All right. Well I'm gonna I'm gonna handle the next Question actually the next two questions because This is great. I honestly I've been glued to Twitter all day, but this is the first time I Caught this and I appreciate thank you Barbara for bringing this up The flag over the White House is upside down. Can you ask why which we just looked into I Know the meeting, but is there more to it? Yeah there is and that I think this This ties into Anita's question as well Have you read the Durham report yet page 84 explains Hilary's part in May 2017 Will she get hers and I think this is all This is all tied together That's why the flag is upside down Shit's hitting the fan It's all coming down. We've talked about this on our predictions for a while This was one of my mid Year predictions about Biden that It's going to get exposed that You know like the Durham report If it wasn't for the Durham report the outcome of the election would have been completely different which is Why Trump will be in office by The first week in September Been predicting that for a while And it looks like this is coming to fruition So what's going on? well You got you got Biden sitting there with his cake wanting to eat it too, but it ain't happening It ain't happening His world is coming down We got regret failure disappointment for the Biden regime and that includes Hilary Obama all these people all the FBI agents that colluded together That were busted on this Durham report We're looking at transition and change. This is what I was telling you guys about with what will be happening By the first week in September Just a prediction for not this for entertainment purposes only to But yeah, I see something big happening Transition and change and remember we also were asked about Hilary They're all getting They're all gonna have to be held accountable There's no escaping this one We got new beginnings And I know Ali's thinking something perverted on this card She's smiling I Well, we got the fool in new beginnings, so yeah, bring it on that's when Trump comes in on In September, so it's gonna be relatively quick. Here we are. I mean, it's the middle of May So we got June July August. We got three and a half months and I believe that Trump will be reinstated by the first week of September So yeah, so what what we looked at here was the meaning of that upside-down flag and what's gonna happen with Hilary We got them both covered on that so Yeah, justice will prevail. That's what I have. What do you have my love? You were right in what you were thinking yeah Um So and when I am through the dice it came up with five Mm-hmm.  Who believes that there is some connection to They were waiting until they were bored with situation and That bill had finished. There is some connection with that So it would be very interesting to find out when that flag changed Was it at the time of that changing, you know, or you know, is it building up to that? That it's it just seems as if there's there's a link to that Um, so I feel as if there's also a link with this So this I'm not doing the Durham before am I I'm getting confused now because the Durham reports up there So I'm doing the the flag The flag and then what I ended up doing was adding Hilary in there. You don't have to do that Together can I go back to the flag one first? Yeah, so there's something to do with the finances Pat situation with finances has finally changed There is something that has flipped over I don't feel as if it's made public yet Well, you will it obviously hasn't and but that is going to be Happening This is it's only the financial situation at the moment is very temporary And it will be changing So that's what the five means I'm here. It's like it's all it's all trading when I look to the Cods Regarding the flag situation I Feel that they have actually Taken in I Feel all the people that need to be I feel as if they have been given, you know, like they were all giving a letter At the funeral, I think it was what the bushes funeral Father Bush for it funeral and they were all given this letter It's official document and they all opened it and you could see their faces Something happened They've all been given this this letter So you may you may see them scatter You may see them try to run so it wouldn't surprise me if they start going on holidays and and You know getting away or becoming ill or that sort of thing and it's all of all the cover-up because it's it's it's happening That's that's what I'm seeing. It's big big stuff. Yeah, so that's what I got. I Did obviously the Durham report You know, I only know a little bit about it, so I can't really say too much really But everything has been exposed It's like, you know, all these nails on the coffin for mr. B Is just coming thick and fast, isn't it? I mean, you know, there is no way of getting out of it now Can't they can't it's all all been done Anyway, that's that's what I get Come back my love come back. Oh, we have a spammer. Oh, whoa. Oh, whoa Bashi, I will bashi. I'll be right back then. Let me handle that So, hello Simone. Hello. Hello and Sharon. Hello Sharon and Shannon Tracy. Hello It was yeah, it was the bushes funeral. Wasn't it Tracy? Yeah, I Saw other picture of that going on So I feel as if they have been handed a legal letter and it is linking to stepping down And it's linking to you're done. That that's what I see It's it's a it's a big thing Yeah What is the next question? So let's go back up So Okay, yeah, I got this as well. I hope well, I didn't get it I didn't get the information I heard about this I'm getting the news that UN troops are going into northern Alberta homes that are at work Evacuated due to the internationally set fires Doing gun grabs or I don't know about that Wow That's a big thing isn't it You see this this all could be part and parcel It's like if it's end game and they're now going they're running They're running scared All of that would make sense really so Yeah, that's awful though for people Affected directly from that So where did the IR with us whistleblower disappeared to howdy to all? Well, hello Anita Okay, so when Greg comes back, we'll have a look into that Okay And so JB 2020 is listening but without the keyboard that's okay Country in distress. Yes, Cynthia. That's what it says about the upside-down flag. Oh so So my Canadian flags on my car upside down. That's interesting That's interesting. So, yeah Yeah so Anita Zelensky and Didn't have announced Will work to stop the war for this work. Oh Announced Africa All this work I feel as if the war my my guides are just telling me that this is so close to being over anyway Um, it's it's nearly nearly done dusted So I don't I don't feel as if any other outside influences need to happen But I do feel as if they've all Signed this new treaty to do with money So, you know the The Ukrainian people are going to be so much better off. They're just going to be you know, as we all are When this new system takes place Financial system Okay, I'm I'm not really sure about this question From Anita where did the irs whistleblower disappear to because I posted God There might be a delay because you're getting cross with me for saying and I I'm not deliberately doing it love I understand. I understand. I'm no I'm good So Anita is asking where did the whistleblower disappear to I posted earlier on Telegram The irs monday removed the entire investigative team And it's long-running tax fraud probe of first son hunter biden and alleged retaliation against the whistleblower who recently contacted congress to alleged cover-up in the case so As far as I know The whistleblower didn't disappear to anywhere Am I missing something? I if you want to answer that question, I don't understand this question I don't think they did. I don't think the whistleblower disappeared anywhere It's a non-question If you want to answer that I don't know enough about it. Um, I know that um, there was And in the um the biden thing a lot of the people a lot of the whistleblowers there have disappeared Um, there is one crucial one though that is uh remaining and that person is ready to testify so um With the with the biden thing, but I don't know much about the irs one I'm afraid Yeah, so sorry Yeah, that's can't can't really answer that one. Sorry That's okay I need to get another question though. So uh, so once getting Putin have announced africa will work to stop the war Will this work? um There's a there's a lot of chat going on about that uh a lot of people are I honestly You know the card that came out we got the uh page of swords and I I don't a lot and along with uh justice as well um and the Ada pentacles um I'm still not seeing anything. Let me pull a few more cards here because I'm I'm still not seeing anything definitive in in this Uh, well that helps to understand Yeah, okay, so um there is betrayal and deception. Uh, so That's that's what I'm pick picking up mainly off of that Uh, it's It's basically what I'm getting out of this is it's smoke and mirrors look over here while this shit goes on Because not only is the Durham report implicating a lot of politicians and important people in the united states We're also going to see how Other foreign nationals and leaders are also involved with this along with hunter's laptop. So You know Zelensky's saying look over here. Don't focus on me and barisma and everything else that's been going on Or the derma report look over here. I think it's smoke and mirrors That's what I have Okay So, um, I feel as if it's soon going to be announced. It's like a celebration is on its way Very very soon. It's like yes Um, this is all sorted. This is all all done So it could be that um, mr z here or z um is going to be um Also implicated in all of this nefarious stuff. So it could be that all of them Go all together. So all the top people Are just all taken out and then mr p Um is put in power Uh without any more W. A. R So that that to me would make sense with what these cards are showing me Yeah, um I I really feel as if you know, every Everybody's such a better off with the the new financial system and they a lot of the uh people in, um, you They don't understand They don't understand what has been really going on at the top of it like um, you know, if uh if there was people coming over here and trying to you know It's like release people from You know, these uh these elite people and it's like well, who are the elite people nothing's going on What are you doing? They're gonna attack the people that are trying to help Um because they don't know and that that's what I think is um happening But I feel that all the information is just the more information that's coming out all people are going to go on this This they are anymore. Um, not now the situation um, so I do feel as if um a lot of uh The soldiers are just going to be going For then i'm done We've also got um a 10 and 10 is completion 10 is done completion And so it's also really really good Um completion self worth happiness. Yeah, all is good. Um, it's done. It's done. That's what the uh diet is saying about that about that particular So i'm not picking up anything about africa by the way. This is just about Um the end of the w a r That's it Okay, well that sounds like smoking mirrors then you know because if you're not picking up anything You know look over here is what they want us to do and You're trying to extend extend it like it's just going on and on and on and it's not it's coming to an end They keep saying that mr. P is really really ill and he looks so ill and he had a mark on his neck and he He has this mark on his and he had this and this it's like um They're just just trying to you know make him look weak and he's not weak at all And if you notice In mainstream media in mainstream Media they're saying about um You know every photograph of mr. T now is where he's pissed off. He's very angry. He's very upset There's no more of him smiling anymore Or mainstream media. Have you noticed this? No No, but that's not surprising. Is it you know, they're trying to control the narrative Yes Yeah Don't go far Because this question I I got an answer instantly It's former president carter still with us. You're saying no. I'm saying. Yeah, I got ace Ace of swords. Yeah, he is it's not I'm not sure about it Because we've got some some cards that are yeses and cards that are noes. So um Yeah, I'm sure about that we've got uh We've got ten again, which is completion which is an end, isn't it? So I'm not sure Okay All right Okay Um, yeah, mine was pretty quick Um, our next one comes from brian up in syracuse new york Will america go into default if the us does not raise the debt limit Will america go into default? Well The first card out. It's pretty bad. It's a financial loss and poverty so, um justice will eventually prevail um, and and and and they're gonna they're working on something to have in place When it does happen, but ultimately, yeah um America will go into default. But like I said, there's there's something it's already it's in the process of Taking place of it. And I don't think it's the Sent cbdc. I don't think it's that Hopefully it's um a gold bag currency That's what I have okay, um Everything is in motion. Um You know, they're actually It is part of the process that they want this to happen. Um, and so the debt the the debt limit Um, it's like, um, not raising that it's like they want them to get to that stage Wasn't mr. B at one point begging For this to be raised at one point and he was he was campaigning a lot and you know doing this to You know online by the way Yeah, but anyway He was doing this because he was so desperate, you know, giving everybody the guilt trip that it had to happen Um, but I do feel as if this may be the transition that they've been waiting for is they have to let it fail And it has to be on mr. B's watch And then they can bring in this Good fortune. Ah All right So it's like somebody coming to the rescue mr. T coming to the rescue His status when everybody gets the gets the money. So I do think everybody's going to get something I don't think it's going to be like you know Nobody wants to go to work the next day. It's not going to be that but there is going to be um, definitely that everybody will be Better off and I do think it will be a global thing. So I think it may start the us Is going to be around there So, yeah, the money situation I deliberately left the cards Um, I switched the cards up before I did this I don't you should do reverse readings. So this time I said, okay, let's do reverse readings just for this Okay, because obviously You know, um This is this is different and this card came up upside down the ten of pentacles upside down Which means that um, the money is changing So That's what I'm seeing and I don't you know when they warned everybody with the computers. We don't Don't know what to do when it goes from This year to the next year. We don't know if the computers are going to fail Or this is going to happen because we don't know if the computers will be able to You know catch up with this. I can't even remember what year it was, but it was a transition year um, you know and It happened and there was no problems. I think they're just warning people that there may be Um issues and that's why they're saying have some cash in and make sure but I actually don't feel as if there's going to be any Problem at all. I feel as if it's just going to be very smooth Very smooth and there's going to be time for you to cash in your old money When then and the new money will just come come in. So it's like, you know, when they released, I don't know if it's Same in the USA When we got the new plasticky money um, you you're like given six months, I think and to get rid of the old money And for that to be replaced and then after a certain time it's not valid anymore. So you can't cash in on it Um, so I feel as if it's just going to be that it's just going to roll out But I you know, I don't feel as if it's just going to be digital money. I think it is going to be cash as well It's going to be some Something it could even be, you know gold pieces, you know It's going to be or something covered in gold It's going to be worth to whatever You know physical worth to it. It's not just a piece of a promise It's uh, it's different. So yeah, it's not a bit long-winded, but that's what that's what they told me So, yeah, well first of all, you know seeing you do a reversal I've never seen that For as long as we've been together. I never never seen you do a reversal card. I don't But I I said I will do them For this that's what that's what my My guides told me that I was to do this time Well, how appropriate I thought so Yeah, and uh the plastic money. Yeah, we don't have that. We actually have paper Currency paper bills It is paper. It is paper, but it you can't fold it This our notes you can't fold them yours is definitely it feels plasticky Like should I tell you let me I know exactly what you Yeah, but other people might not So this is a five pounds It's it's not paper.  All right. So well, thank you for that Um moving on we have a question from Barbara will I I don't know who you know who I We know Who's ie we well we can look into we Uh Anthony winner, um, well well he come out. I'm guessing will he get exposed? I've been I've been big on you know parading for him to his laptop to get exposed because You know By now many of you have heard of frazzle drip Well, that's on his laptop He and his wife at the time whom a Aberdeen Aberdeen was a um an aide to hillary clinton and they kept a A bunch of files and a bunch of insurance policies so to speak In case something happened To one of them They had this insurance file basically against hillary And a bunch it could have been a bunch of the other cabal as well that laptop a bunch of Detectives in new york city city saw that I think there was 10 10 different detectives and Just about all of them had to go see Go get psychiatric health afterwards Because of the gore That was on there and I can't say it here. I can tell you on thursday night What huma Aberdeen and hillary allegedly did this for entertainment purposes only But it's really gross what they did with this child And like I said, you know it has something to do with frazzle drip Very gory This has to come to light You don't have to watch it You don't even have to believe it Be careful if you are You know on the you know, it's and you'll try and you put that in the search engine Because unless you're ready Um, and you've got a strong stomach. Um I wouldn't say to to do it. I really wouldn't but you might want to look it up and see what it's about And read what it's about instead of actually watching the video and then I'll put images up And don't put it on you On youtube It's hideous. It's hideous Um, but yeah, that's that's how bad it is Um, so will he get exposed? Well, I've I've you know, he's got financial loss poverty another one Judgment is coming Judgment's coming and with that transition And the ace of swords. Yeah, he will get exposed.  They're all coming out finally Finally Truth is coming out Hang in there folks. Have you because it was during the video picture? Um, or you was doing a video, wasn't you? I can't remember every single week you did it and you were looking at the silver ratio and you was also looking at um The um indictments and how many were there how many? Yeah, you looked that up recently Uh, the last I knew it was over 200 000. I don't have a specific number It would be good to take notice of it and to see if it does start going down now Yes, yes, it's like upside down just maybe Okay, so, um, I don't know the the willy bit and the weiner Come out next. Oh I say I thought I thought it said will Ie and weiner, but it was willy But I don't know who will he is either No Could be a william. Is there a william in in that anyway? Yeah, what I thought was um, that yes It will be exposed, but it's going to be right at the end It's going to be when everything When the other stuff is if this is too much for people to cope with right now Um, because if when you open up some you're going to open up all Um, and and the people people aren't ready yet. So I do You feel as if it will be exposed but not yet What I got Okay, short and sweet All right Hello, michael And elsie. Hello, elsie Our next question comes from lice Um I know we're like Looking over the I've got no I've got a joystick going and It's all going everywhere Allie and craig. I have a question about our current danish prime minister The one that ordered the killing of many million Minks who are minks?  No um, yeah, I don't either but I'm addressing guessing it's a group of people and ultimately um well Yeah, this You know, there's something going on where her back is against the wall and she's almost has to do it She's being forced into it by the new world order. I do see judgment coming, but that's in the form of Uh, yeah, she will be held responsible for this. This is a global uprising right now and uh, you know and and It's not just the united states. We're seeing the truth come out in all countries You know a lot of this will center in the united states, but it expands outwards and uh, yeah, so um Yeah, justice is coming. She will be held. I'm getting that she will be held responsible lice Yeah Allie will be here in a minute to answer you as well Our next question will be coming from Barbara and Well, it's not really a question I just had an on 9.5 solar flare about 6 p.m. Today. Okay I think that's more of a comment Hello, my love Hello, my darling. Um, I just did the dice on this and And it because I don't understand the minks or anything. Um, but um But I got an 11 And 11 is linked with angelic energy So the angels and the higher beings the offworlders are all Dealing with this so it could be a karmic thing That is going to be coming about with this so it could be that there might not be um Legal justice, but there could be something else going on behind the scenes because there's more than one way to For somebody to get there what they deserve So, yeah Do if that helps or not or that's what you want, but Yeah, but that sounds absolutely Disgusting and despicable Anybody, you know ordering millions of people to be uh it's just Or everybody should be made accountable Lisa Lisa samuels could not be on on with us Because usually her head's like way down here She always Yeah, yeah That's funny. Um Our next question is from Anita gal mtg Marjorie Taylor green has been at the treasury department looking at suspicious activity reports sars So far she's found money moving from ukraine and to other countries to the biden family llcs So is that a smoking gun? Yeah, it sure is um Painful endings coming up More painful endings ten of swords Ten of swords and the three of swords Uh, you know heartbreak emotional pain painful endings all that stuff followed by the sun So positive outcome after that but first Painful endings there will be pain and that's for the cabal the biden family um everybody that's been working against Uh humanity's best interests Pain is coming But not for you good folks out there Celebration's coming for us and that's where we saw the sun card And the happiness and the celebration. So this is coming for us Got the sun card again loving it digging it Digging it Ellie's still pulling cards right now. So she'll be here in a second. There she is All right, so um So, obviously, I mean, you know, this is the one that I said that you know from a lot of the whistleblowers That there are a lot that have gone missing Or they have been they're in court. There's been Lots of different reasons as to where they might be but they're not But there is one particular person Who um can bring this about still so they haven't lost everything but they are definitely Playing games. Um, obviously, um the the b family. Okay um So what I got was obstacle. So that's I got with the dice. It was a nine It's an obstacle obstacle. So Um miss green is obviously, you know, she has got obstacles there We do have the the tower card, which is an eruption. Um, I can honestly I don't usually see this And the only time that I'd ever give this in a reading would be in the circumstances, but I will I do see a A um taking of life. I do see that Um, I don't know who that will be but I do know it's one of the bad people Um, um the people. Yeah, so I feel as if there will be a passing there I do see this being a A ritual thing and I believe that it will be a scapegoat thing You know putting all the blame More directly on on that. So, um, I feel as if this is all in the works there Um, yeah, it's like somebody who's controlling everything or did control this Yeah, so don't be surprised. You don't see this coming up. Um, but uh, the balance it the the balance is trying to come about. Um I I feel that this will be successful. I'm going to ask the dice. Will this actually be successful So the case here Six 11 12 which is a three Which is celebration. Yes At the moment news get ready for success. Um, there is more layers to consider. So from this there are other layers that will also be um successful, so yes I've actually, um For my primes for this mystery gift this month. I've added in my dice game with the dice. I've put it in there. So As well as other other gifts Yeah That's sweet awesome All right, um Anita with another question She's like a question Oh, I need to we love it Um, it's been one year since taylor hawkins from food fighters died Was it a suicide or a murder? Wow, I didn't even know that that was that was coming up and I did pick up just now The word s didn't I somebody taking their own life and then this question came up Okay well um His back. Well, I got a couple Um interesting cards on here. He got the nine of nine of wands So his his back was against the wall Uh You know as ellie would say it's a test of faith, but He got the he got the tower card after that And then the six of swords which is transition change You know, it kind of sounds more like a suicide if anything, but i'm not really picking up suiciding What i'm picking up is that There was a lot on his plate And he It was more of a It was more of an overdose but not a suicide you can overdose without it being a you know an intentional suicide you know Just a lot on his plate. He might not have kept track of How much he did of this substance or that substance and it all added up and he ended up dying afterwards But i'm not really picking up that it was a suicide or a murder Um God what a talent to Just you know very very talented musician drummer And it's such a shame Such a waste, but I'm not picking up Not picking up. It was a suicide just there was a lot on his plate and he wasn't really paying attention to everything that he was doing and it all accumulated Into a death. That's what I have for entertainment purposes only um I was picking up I threw a um Sit 12 14 14, which is um five um Fives are always obstacles and things there are always kind of you know things that um Are problems and battles and that sort of thing So I do pick up that he was definitely battling with a lot on his plate. There was a lot of pressure I don't feel as if he was um happy with some decisions that were being made By either his team above him Um, I am picking up actually that there was somebody at fault and this person knew That he shouldn't go any further with the intaking of more um More drugs really um and didn't say anything and allowed it to happen. So I feel that it could have been prevented But I don't feel as if it was a deliberate suicide No, but I do think that this person who was above him thought well, this is actually going to be easier If isn't here anyway Because they wanted to take things in a different direction or they were making some financial decisions that um, he wasn't on board with Yeah, that's what I thought and you know what um co-create happiness um said died suddenly from you know, what? um, and it could be a conglomeration of Everything like that, but I'm not feeling neither one of us is feeling that it was a suicide former I really feel as if there were um other drugs in his system as well But obviously interfered with that that as well because I definitely saw um It was a needle basically. I saw a needle Yeah, it's my understanding that you know, he heroin was one of his I didn't know that Yeah, yeah Well, we made it through the evening my my love We did We did um We would like to invite you To join us on thursday evening at seven thirty Here on youtube and facebook. We'll just do a little Check in and say hi. How are you and we'll give you the link to Rumble to join us there where we can talk about everything and anything completely uncensored. So Um, we're looking forward to having you join us there If you think we're opinionated now what was then I know It's you know what and we it's great that we attract so many people on on rumble for watching it People dig the ability, you know to have open sensor-free chat Which we should be able to do anyway. I mean, you know You should So, um, is there anything you would like to wrap up on my love No, I've got about 10 to to 12 days left of working days before I go to um America where there I'm going to be opening up some work days But not very many So if there is anybody who does want to book a reading with me before I go off to See this wonderful man, um, then there's only about 10 to 12 days To do is from yeah go to psychic alley dot net and and book it yeah I'm trying to find my link so I can Post a link for it's down there on the screen HTTPS dot dot forward slash forward slash psychic alley dot net But you can actually get if you just put psychic alley dot net it does come up So, yeah I appreciate my lovely sexy husband There we go That's what I wanted Book a reading with alley. Yeah And uh, check out in 5d.net for awesome shirts like this and more For 24 99 or less and if you're a patreon member you can get five dollars off um, so Join me on patreon at patreon.com slash in 5d Also, join us on rumble and and uh telegram because we're We got stuff coming out That is amazing that we can't say elsewhere like here on facebook Uh, so I've already posted those links in the chat. Check it out telegram And Rumble, so yeah, hope to see you guys on Thursday night With this beautiful goddess Myself Thank you Anita Anita Um, they look presence. Yeah, there's one tier. I think it's 22 dollars 22 You get sent a mystery gift every month. So that's what I'm doing So anyway, yeah, love to all and I will see you On Thursday.  Thank you as well Uh, just want to say that we both appreciate you and love you guys all so very much Thank you for being part of our in 5d family And we're sending lots and lots of infinite love and light from our hearts to yours So until Thursday, we'll see you back here in two days. Okay. Yeah Yeah, take care Love you all. Bye