It's time for the Lawn Jean Chronoscope. A television journal of the important issues of the hour brought to you every Monday, Wednesday, and Friday. A presentation of the Lawn Jean Wittner Watch Company. Maker of Lawn Jean, the world's most honored watch, and Wittner, distinguished companion to the world-honored Lawn Jean. Good evening. This is Frank Knight. May I introduce our co-editors for this edition of the Lawn Jean Chronoscope? Larry Lasser and John B. Oaks from the editorial board of the New York Times. Our distinguished guest for this evening is the Honorable Chauncey W. Reed, United States representative from Illinois. Seems fitting, doesn't it, that one of the long-time representatives of the state of Illinois in Congress should also be one of the four most congressional experts on the man from Springfield, Illinois, Abraham Lincoln. Representative Reed, do you agree that during Lincoln's presidency things were tougher than they are now for Eisenhower and his presidency? Undoubtedly. The country was torn in a civil war, which of course is really worse than any other kind of a war, a foreign war.  Do you think the country is much more homogeneous now than ever before? Oh, yes. Do you think that he had as much trouble with the Republican Party in his day as President Eisenhower is having today? I think he had more trouble, yes. Did you, as a conservative Republican, feel that Lincoln was radical in some of his views? No, I think he was rather conservative in his views. He didn't believe in amending the Constitution any more than was absolutely necessary. He, of course, he took the radical, what was called then the radical view, in that he was for freeing the slaves, which was then considered the radical view. But it afterwards turned out that it was not so radical. Well, he also thought, I believe, that the Mexican War was wrong, didn't he? Yes, when he served in Congress he was against the Mexican War. That was under President Polk. And after he had voted against the entering into the war, but after the war had been voted, he then voted for every appropriation to carry it to a successful conclusion. What about Lincoln's record in Congress, Representative Reid? He was a member of the House of Representatives in, was it 1847? 1847-48. What was his voting record like then? Did he support the party? Yes, he was the only Whig that was elected from Illinois that year. There were seven in the House and he was the only Whig. The others were all Democrats. But he supported President Polk who was a Democrat in the conduct of the war. And he voted the Whig line pretty much in his entirety. You say he was a strong party man and moderate? Yes, he was a moderate. Or a left-wing Republican? No, of course there weren't any Republicans then. He was a Whig. Well, if he were alive today, do you think he would have been a Republican? Why? Well, I think that he would have espoused all of the things that the Republican Party stands for now. What about the Senate? He never quite made that, did he? No, he ran for it twice. And the first time that he ran for it, he could see that if the legislature cast any votes for him, that they would probably defeat Judge Trumbull, who was then a senator. And so he pulled out of the race and let Trumbull be elected. The second time was when he ran against Douglas. And he received the popular vote at that time, but the state was not divided or apportioned evenly. And Douglas received the majority of the members of the legislature. And of course the Senate had one half of their membership that didn't run for reelection. Of course they were holdovers, and that together gave Douglas the majority. We were talking before about his term and the House of Representatives. But what sort of pay did Abraham Lincoln get in those days? He got eight dollars per day. Well, so you're asking for a little more now, aren't you, as the rightful member of the Judiciary Committee? What's that going to be like? That will raise our pay from 12,500 per year to 22,500. Do you consider that to be inflation or the value of a representative now? I think it's the value of a representative. They haven't been raised for many years, and the work of a representative is much greater than it has been. The sessions of Congress are much longer, and those who have professions or businesses and who formerly could go and make a little money at their various professions and businesses can't do it now. Mr. Reed, you spoke of Lincoln's difficulties with his own party and his problems as president. Do you feel that the party nowadays is in any danger of dissolution or splitting? I do not think so, no. Do you feel that there is a right wing, left wing split within the party at all? There is a division. It's not a very marked division of the, you might say, the die-hard conservatives and the very strong liberals. But the division is not very marked, and many of the conservatives are taking the liberal point of view now.  I think we're molding the thing together. You include yourself among conservatives who are taking the liberal point of view? Yes, I think I am. What about the political attacks that Lincoln faced in his day, Representative Reed? Do you think they were more bitter than they are now, or are things about the same? Well, I think they were more bitter. The cartooning was very marked in those days, and the candidates were rather bitter in their campaigns, I think more so than they are today. Lincoln always seemed to have a theory, didn't he, that, like Harry Truman, that if you couldn't stand the heat of the kitchen, you'd better get out of it. But he always liked to lighten things with a laugh, didn't he? Yes. He could, he could get warring factions and bring them, they'd come over to the White House to see him, and they'd have blood in their eyes. And Lincoln was able to tell them an apt story, and they'd go away laughing, although some of them didn't like it. I recall that he was asked what he felt, how he felt it was like to be present when he said it was like being written out of town on a rail, that if it weren't for the honor, he'd prefer to walk. Yes. Representative Reed, what about yourself, as a ranking member of the House Judiciary Committee now, aren't you backing a bill that would reduce income taxes to some extent? That's correct. The bill would limit income taxes to 25%, and would do away with inheritance taxes, they would go back to the states. The 25% could be raised to 40% by the Congress if three-fourths of the members of both houses voted in favor of it, and if in case of a national emergency or a war, they could raise the limit entirely. Well, now it's been estimated that that would cost the Treasury about $13 billion that Representative Reed, I imagine that you're a believer in a balanced budget, how do you make up the difference? Well, we have an idea that with the income tax raised or lowered, that the Congress will have to lower its expenditures because it won't... You, for instance, have been opposed to foreign aid on any sizable scale at all, would you take that as one of the areas of cutting expenditures? I would take that, regardless of whether the income tax amendment goes through or not. Representative Reed, would your income tax amendment be a 25% income tax on everybody's income? Yes. That this figure must not be exceeded? It will not exceed that. No, it can't go above that. You, as a real admirer of Lincoln, of course, would recognize that he was a strong president, wouldn't you, Representative Reed? Yes. How do you think he would have felt about the Bricker Amendment as an example of a limitation on the power of the presidency? I would have no idea how he would have felt about that. That's a problem that your committee may have to handle? Yes, we may have to handle it. It's an amendment, and all amendments come to our committee. Well, Representative Reed, do you think that the fact that Eisenhower has gone to the Congress to ask for authority to prosecute the Formosa War means that the Bricker Amendment has been met and challenged and done away with? No. No, that was merely, he would not have had to come to Congress at all if he didn't choose to do so. But he preferred to have the backing of Congress in any act that he may take to preserve the situation as it now exists in Formosa. Well, do you think that was a political stroke by President Eisenhower, or was that actually a move to make the country homogeneous behind him? I think that was, the latter is correct. And do you think that the Bricker Amendment will still come up in this term? Well, I'm sure it will come up. I don't know how far it will get. I understand that Senator Bricker has amended it in some respects, and perhaps done away with the objections that the President had to it. How do you feel about it yourself? Well, I'm rather non-committal on it. I don't know yet how I would be on it. I honestly don't know how I would vote on it. Well, I suppose you used your fondness for Lincoln as a touchstone on many things. I do think that there is a room for some sort of an amendment like the Bricker Amendment. I think there's room for it. Because I don't think treaty law should supersede the Constitution. Thank you very much, Representative Reid. Very glad to hear from you tonight. The opinions expressed on the Launcine Chronoscope were those of the speakers. The editorial board for this edition of the Launcine Chronoscope was Larry Lusser and John B. Oakes. Our distinguished guest was the Honorable Chauncey W. Reid, United States Representative from Illinois. Launcine is the world's most honored watch, and by any standard of comparison, Launcine is ranked as the highest achievement in modern watchmaking. The greater your discrimination, the greater will be your appreciation of the quality, the beauty, and the unsurpassed performance of a Launcine watch. Now here are the facts. Among the finest watches of the world, only Launcine has won ten World's Fair grand prizes, twenty-eight gold medals, highest honors for accuracy at the great government observatories, and yet, in spite of surpassing quality, you may buy a fourteen-carat gold Launcine watch for about one hundred dollars or even less, a gold-filled watch for as little as seventy-one fifty. You may choose from the largest variety of styles and types of any watchmaker in the whole world. A quality considered, a Launcine watch represents the highest value in all watchmaking, and may we say that if you pay seventy-one fifty or more for a watch, in fairness to yourself, insist on getting a Launcine, the world's most honored watch, the world's most honored gift, premier product of the Launcine Wittner Watch Company since 1866, maker of watches of the highest character. This is Frank Knight reminding you that Launcine and Wittner watches are sold and serviced from coast to coast, by more than four thousand leading jewelers who proudly display this emblem, agency for Launcine Wittner watches. The Boy Scouts of America deserve our cheers on their forty-fifth anniversary, building for a better tomorrow.


The Rocaster Pro 2 firmware update 1.0.5 adds some new functionality which changes the way that we can use the Rocaster Pro 2 with applications like Ecum Live, Zoom, Teams and Discord. And in this video I'm going to explain to you what those features are so that you can understand how best to get things set up for your particular use case. And that's the key thing here, there is no one size fits all, it's more about just understanding the concepts so you can figure out the best way to get things set up for exactly what it is you want to do. I will of course be sharing my setup and what I'm using it for and how I've gone about that. And in doing that hopefully you will get a little bit more insight of how you can get things set up for what you want to do. Now this isn't going to be a full overview of the 1.0.5 release, indeed I've already made that video I'll leave a link to it down in the description as well as how to actually sign up for the beta program because at the time of recording this is still a beta release but it may have been fully released by the time you watch this. So let's get into these new features shall we and they are all related to the USB cables that you've got on the back. There are two USB cables on the back of the Rocaster Pro 2, let's call them the primary and the secondary. So the primary is the one that you would need to connect to your computer in any case if you want to maybe download the audio if you've recorded any to the to the device on the SD card on the back or to program the smart pads. You can do it on the device here as well but if you want to do that through the Road Central app you would need to be connected through this primary USB cable, the main first USB cable. However that's not what we're talking about today we're specifically talking about the audio channels that we've got and there are in fact two audio channels on that first USB cable and they are called Rocaster Pro 2 main and Rocaster Pro 2 chat that is how they appear on your system. There is also this second USB cable you don't need to connect that to your computer you could do though you can connect both of them or you could connect this to a second computer in fact and I'll be talking about why you might want to do that a little bit later as well. I do have both of these cables connected to my computer though and that effectively gives me three channels which you can see down below Rocaster Pro 2 chat main and secondary. So why have I got six down there? Well that's because there is actually a new feature that has been added and it doesn't give you six channels before you get excited but it does actually change the behavior of that main channel so you can see whereas before in the previous firmware versions it was just Rocaster Pro 2 main and now it may either show up as multitrack or stereo so I think it's worth actually just covering this part first so that you understand exactly why that might be. So in the previous version of the firmware basically over that first main channel it was actually sending out the multitrack mix so it was sending every single individual track over that USB so let me just maybe explain this a little bit better. If I come into the settings and I go to outputs then we've got multitrack. Now maybe it's worth explaining this from a point of view of just recording so when you are recording to the device itself you've got basically four different options or three and a three and a half maybe. The first one is if you have this set to off it means there's no multitrack recording it's just going to record a single file whatever inputs you've got coming into this you got audio sound effects on here maybe you've got two or three microphones plugged in and then you've adjusted different levels of different things on here it's just going to record those down to a single file so that would be multitrack is off but then you could have a multitrack on so you might want to record all of the individual tracks so that you can then do something with them later and the normal way that you might do that is to use this prefader and what that means is although you might be adjusting levels in here maybe you're live streaming or something like that and things are going out and you want to make sure the mix is all right but if you're going to go ahead later and do some editing and maybe repurposing things then you might want all of those individual tracks without all of these different levels adjusted and so that's what prefader is basically prefader so these are the faders before anything has been applied to them it's just going to take all the raw signals and then record those. Now you can also here opt to bypass processing as well so bearing in mind that in the Rocaster Pro 2 we've got a lot of really powerful audio processing that we can do to the signal as well and so you can actually turn that one on to bypass that so that then it's basically really is just going to take the complete raw signal so you wouldn't have any compression or anything like that that you'd applied to it you would then be able to do something with those after and maybe apply them after the fact. The other option though is post fader and that is basically whatever you've got things set here it's still going to record all of the individual tracks separately however if you've you know lowered the volume down here then it would be lower in the recording as well so hence the little warning sign there do you really want to do this because it's going to affect the signal that's been recorded so that is nothing new that is just to explain to you the difference between you know multi-track or not multi-track well now over on the USB so that was on recording previously on USB we only had the option of prefader or post fader we didn't have the option of it just being a stereo mix that is the or one of the new features that's been added in in 1.0.5 now why would you want that and which one should you have you may ask well if you are using a digital audio workstation a door on your computer and you want all of these tracks going into it so that you can then you know make adjustments maybe you're recording it maybe it's going into some other application adobe audition or something like that where you're going to be you know using all these separate tracks and you want to have full control over them then yes you would want something that's either prefader or post fader going in a multi-track mix going in however if you are if you don't know what a door is then likely you can just switch this one off or if you don't use one you can switch what this off certainly i am going to leave this off because all i want is a stereo mix going out into my computer because i'm just going to be basically taking everything that i've i've got going on here i just want it all mixed down into a single stereo mix that's what's going to be used as my input for e-cam live for zoom for anything else i'm not doing any other fancy audio so for me then i'm going to switch this off on the usb what you do on the recording is is entirely up to you but for me i'm going to switch that off because i don't really have a way of even recording the multi tracks so that is that is what i'm going to do there if you watched one of my previous videos about the best setup for the rocaster pro 2 with e-cam you may recall that in the e-cam live settings in the audio tab there was this option here to map input channels one and two to left and right stereo that was a requirement before because it helped get around an issue where previously we were only getting the multi track mix out we weren't having this option of the stereo mix that was the solution to stop this had a slight issue that where the faders even if you put the faders down you would still have the audio coming through so toggling that one on there fixed that issue if you had been using the rocaster pro 2 before with some things that work in browsers there was also an issue there with this multi track mix coming out over the usb however that has now been solved with this new setting so if you've come into your rocaster pro 2 and you've changed that to off then you can still map channels one and two to left and right stereo but it's just not quite as essential but since you've got a stereo mix going out it would make sense to do it so i'm leaving that on for now so that is all the about the different mix now i should say then that just coming back to these names what you'll see is if you have got the multi track on as i the pre fader of post fader it will show up as rocaster pro 2 main multi track whereas if you've got it off as i have now it will show up as rocaster pro 2 main stereo just on that main channel there what you need to make sure though is if you do set your computer up and you've got different you know applications like ecam live for example if you've got it set to one of those and then you go into your rocaster pro 2 and change from you know pre fader and post fader change it to off then you might find that whatever devices in or whatever applications you've got in your computer of then you know defaulted to whatever your audio default is so if i came into ecam for example selected rocaster pro 2 main multi track as my microphone i came in here and then i switched this over to switch it off then that that device would just sort of disappear from my computer and ecam would just go to whatever the system default was so just make sure that you get this set up as you want it and then set your audio settings but that is not the most exciting feature the exciting feature is the fact that we now have mix minus on all of the channels and in fact we have something even better but i'll come onto that in a while first of all what exactly is mix minus well if you are using the rocaster pro 2 as both an input device and an output device for a particular application let's take zoom then you are i've got in zoom you've got the rocaster pro 2 set as your microphone but also as the speaker the audio what you're hearing the audio from and so zoom is going to be sending the audio from all of the other participants sending that into the rocaster pro 2 it's going to be then in the mix of all of the different things that you've got coming into here with your microphone and everything like that and then it's going to be going straight back into zoom again as the microphone and what that means is that anything that the participants are saying will just basically do a bit of a loop round come straight back to them and they'll hear themselves back a moment or two later so what you need to do or what needs to happen is we need to remove the incoming signal on that particular channel from what's been sent down that channel again hence mix minus we're removing it from the mix and then they won't hear that that slap back now you should know that as well you won't actually hear anything in your in your monitors when you are listening to this so it could be that the people on the other side are saying i'm hearing echo they'll always call it echo not slap back but they'll say that and you'll wonder what's going on because you can't hear anything it's because you're only hearing it once but it's just making the return signal for them and they're the ones that are hearing it twice so this applies to any communication app where you're using it as an input and output device so zoom teams discord skype whatever it happens to be it also applies though to applications like ecum live because ecum live itself has built-in sound effects so we might have a movie that we play as part of a scene we might have audio in ecum itself we've got sound effects that we can trigger within ecum from ecum so those would be coming from ecum into the rocaster pro 2 but then they'd just be going straight back in again so once again when you're listening and recording you wouldn't hear any issue but then when you listen to the audio playback you would hear a duplication of anything that was originating from within ecum and that includes by the way interview mode so if you're using ecum live in interview mode this is an issue so that's where mix minus comes in we need to have mix minus switched on on any of these applications that have this two-way audio going on now what i should also say is if you're using these applications at the same time like with one another so for example you might have somebody on on interview mode in ecum live you're feeding that into a zoom call and then there's people on the zoom there as well that are communicating it's important that each single application has its own dedicated channel with mix minus on because bear in mind the mix minus it only removes it for that single channel so we want the zoom people to not hear themselves back but we do want them to hear anything that's going on in ecum so if we had set those both to exactly the same channel then it would be removing everything from zoom and everything from ecum and so the people in zoom wouldn't hear the ecum if that makes sense so you need to make sure that however many different things you have got you have got a separate dedicated mix minus channel for them so whilst on the rocaster pro 2 we do have two usb cables um you don't necessarily have to use both of them you could as i say just have the primary plugged in and then maybe you might want to use the the main channel so just popping those up again so you might have the the the main might be for ecum live and the chat might be for zoom and by the way system audio it doesn't necessarily matter if you have these on any particular any one of these particular channels because it's it's only a one way so system audio doesn't really need to have a mix minus it's only where you are going into some other thing but just bear in mind that if you have mix minus on the system or if you have the mix minus on the same channel as ecum live then in the ecum live settings what you would do is you would just come into here and then you have this broadcast system audio you'd need to make sure that that was still set to either when sharing the screen that's usually the default for ecum so you still are capturing it on ecum but if you had the the system audio on another channel what you would want to do is just make sure that you turn this one off so it says never so the ecum itself is not capturing system audio but maybe you're bringing that into one of the other channels and then you've got that in the mix so one way that you might want to use this is let's just say that you are using ecum live with zoom and you also have system audio and you want that completely separate so that you can have control over that well in that case what you might do is from these three channels down below in fact let me just move the one with the mix just so that we don't start getting too confused if i remove of course i had a 50 50 chance and i removed the wrong one so here we've got these three channels the chat main and secondary what you could do here is you could say well okay let's have ecum live as the main let's have chat as the zoom because people are talking and let's have the secondary as being system audio so what you would do there is you would come into ecum you can see here i've got rocaster pro 2 main set here i've also got in ecum rocaster pro 2 main stereo set as the source just down here as well and then you would go into zoom and you would set that to chat or secondary or whichever one you wanted and then you would just set your system audio to the other one again this is just assuming you've got both of these cables plugged in now basically you've got completely independent control over all of these three channels so you can have them all on a separate fader and what you'd need to do though is just make sure that on your ecum channel and your zoom channel that you do have mix minus turned on so let's take a look at exactly how you do that so let me just get this one out of the way back over to the rocaster pro 2 if i click on the settings and then i click on outputs and then i click on rooting that's the one rooting then here you can see now we've basically got usb one at the top that's main this one is the chat channel this one is the secondary channel and by the way this also applies to bluetooth so if you have got anything connected over bluetooth it also applies to that as well so then you can now choose between main or mix minus and this is what we always did have on the secondary channel but now we've got it on the main chat and the secondary as well so you just need to make sure that for anything that's a two-way communication you've got mix minus turned on they do have something here though which is this extra one here which is custom what that means is they give you basically full control over what you are sending out to each particular channel and in fact the way that this is set up here is simulating mix minus effectively you can see it's this is the particular channel that i'm talking about it's the usb one the main and then down here at the bottom it's got all of the other different channels and it's got little ticks next to the ones that are included in the mix and it's got a little cross next to any that are not and they're sort of slightly grayed out as well so at the moment everything is going into the usb main except the usb main itself so that's effectively simulating what mix minus is it's taking everything in and it's sending everything back out except that one well you could also say uh perhaps i don't want the zoom to be included and let's say i've got the zoom on the chat for example i might want to have a zoom call going in the background uh that is kind of like a back channel where we're talking about stuff uh or having people you know giving me information uh whilst i am live streaming for example and i might just not want that going out into the live stream and in which case i could just simply click on this one and it would eliminate it i would still be able to hear everything that was going on and imagine if i had friends i know it's hard to imagine but imagine if i had friends and i was doing a podcast with them and we were all in the same room together and we'd got two or three microphones plugged in and we were all you know three of us plugged in on our headphones as well what this would mean is that that zoom back channel they would all be able to hear that i'd be able to have full control over the audio for what they could hear but it just critically would not be going out into the mix which was going into ecum live for the recording for example so this is how this routing table works you can basically just choose anything that you want to go to anywhere he says pressing the wrong button so that's the the the way that this works is you can basically just have complete freedom of what is going to where now there is another way to do this though because i'm actually using this as a sort of back channel as well so what the what i'm doing with this is i do have a discord server and in fact if you want to join the take one tech community you can join at take one tech dot i o slash family where we talk about all the sorts of stuff that i talk about on this channel in fact and in fact one of the setups that i'm going to show you in a moment has come about because of a question that was asked in there which was slightly more complex and um a slightly more complex use case shall we say but one thing that i set up in my discord server was i wanted the ability through my channel memberships cue the memberships you can join by clicking on the join button down below any of my videos are on my channel homepage but one of those membership levels i actually have a thing called on air backstage which is basically whenever i'm live streaming to whatever platform it happens to be um i want the ability to have a you know basically live stream into the discord as well so that people can watch live but then also ask questions and i can hear the questions because i always feel a little bit disjointed when i am on on a live stream when i see comments come in maybe i'll look at them a little bit later they lose their context i forget what they're in reference to and it's not really a full conversation there's always the latency to deal with as well even if i think i've answered it i say does that answer the question and then we sit in there waiting while well the internet does its thing and gets the the message across so it is a little bit you know it's not a real conversation is it whereas i saw the opportunity though through the discord and through my memberships to open that up so if i come over to discord just quickly what i'll show you is here we are in the discord here are some of the topics and things like that that we talk about free to join discord by the way just to quickly pop that one up again so you can easily come in here we talk about all the sorts of topics that i talk about on the channel but down here in the members area we have this on air backstage and so the way that works is basically i go live into there before i go live on any other platform but then it just sort of it's just using the e-cam live virtual camera but then when i hit the go live button on e-cam it's uninterrupted into the on air backstage area and then i can do my live stream when i start having more interview guests on and people like that then people in the backstage area will be able to ask their questions and i'll be able to hear them as well and then get those questions answered and then after i click end on the live stream basically it still just continues on in the on air backstage area so then any other questions that need to get asked for the the person we're interviewing or whatever from those members they can get an asked answered i should say as well so the way that i'm doing that though is very similar to what i've just shown you but the thing that i wanted was although i could have used this rooting table if i get the right scene up although i could have used the rooting table to basically eliminate the chat from there you know the discord i could have eliminated that from the main i actually don't want to eliminate it because i want the option of bringing those people into the mix a little bit later so the way that i'm doing that is this if i just come out of here for a moment so the way i've got this set up is i've only got mix minus on all of these channels i haven't used the rooting table for what i'm doing right at the moment i've just got the mix minus on and so in fact the way that i've got it is this is my microphone this is the main channel that's for ecumlive this one is the chat which actually i'm using for discord and this one here is the secondary which i'm using for zoom so hopefully it should be pretty obvious but you just literally go into zoom for example come into your speakers and you can see we've got rocaster pro 2 secondary we've got main we've got chat so i just come in here and select rocaster pro 2 secondary for the both the speakers and the microphone and then if i come over to my discord then in here you just go into voice and video and there you can see i've got rocaster pro 2 chat and rocaster pro 2 chat so there are three individual channels now what i'm doing and i'll come to the system audio in a minute i've done a little bit of a trick there to give myself a fourth channel but what i'm doing then is on the rocaster pro 2 then i've got these four channels my microphone ecumlive discord and zoom so when i am on a live stream i want to be able to hear what's going on in the chat but i don't want it to go out into the mix so if i press the mute here that is basically muting that channel so it's not going out into the mix however it's also muting it for me so i can't hear what's going on you'll notice the little light down there it might not show up too well on the recording because it doesn't pick up the light as well but you can see it up here it's got this little red symbol so that shows that that channel is muted so that would mean that if i was in discord now as well i'd be able to hear the people in discord oh sorry the the people in discord would be able to hear the live stream i should say but we wouldn't be able to hear them so if you want to be able to hear them though you can hear any channel even if it isn't included in the mix by pressing this button here which is the listen button and the thing about doing that though is when i press that it actually excludes all of the other tracks so the idea behind these buttons here these listen buttons is that it's for you to be able to just hear that individual track maybe you might be playing music you might want to cue some music up or something and get to the right place or maybe you want to hear what somebody else is saying and just exclude everything that's going out so for you as the host just this is only on the first channel here the headphones channel you can press the listen button and listen to that channel at the exclusion of all others however you can actually just select multiple channels to listen to so in this case where i've got these four channels what i'm going to do is just actually press the listen button on all four of them now what that means is that i can hear myself back so i can monitor my microphone i can hear anything that's going on in ecamp i can also hear anything that's going on in the discord and i can also hear anything that was going on in zoom if i had a zoom call going so this might be for example running a workshop where i've got people coming in on interview mode in ecamp it's going into the zoom but then maybe we've got a back channel with guest speakers and things like that in discord for example so crucially though this one being muted although i can hear it it's not going out into the mix but the thing about this though rather than using the rooting table to sort of completely eliminate it is this means that if i do have somebody from the discord who i want to bring up and ask a question i probably wouldn't do it for like a back channel if it was a case of you know running a workshop in zoom where i've got guest speakers coming up we'd have another way of bringing them on there but certainly for this idea with the discord where you want to bring people up to ask questions maybe during the live stream or maybe you're doing an interview on the live stream and you want to take questions from the people in discord maybe bring them up on screen as well with ecamp then we could do that then what this means is all you need to do then is just actually take them off mute and then they come back into the mix and you can see that now those are all green because they are all uh i'm still listening to them all but i can just easily take one out of the mix if ever i want to do that same with the zoom you may maybe want to just eliminate the zoom from uh you know the uh from the recording um but you still want to be able to hear what's going on in there but the other thing you can do if you've got it set up this way is they've got this thing in the rocaster pro 2 whereby here i've got these two selected if i select these two as well they'll turn yellow and what that means is that then only they are hearing me and i'm hearing them and it's not going out into the mix so let's just say that we've got somebody in the back channel maybe i'm presenting something or i'm using ecamp for something and i'm playing a video and whilst the video is playing i want to be able to say something to these people in the back channel without it going out into the broadcast i would just press this button and you'll notice that both of these then turn yellow they turn yellow up there as well so whilst i did that you couldn't hear me but it was only going to this back channel so whilst i really love the rooting table and that ability to be able to have much more control over things is really great uh for me personally i'm going to stick to this way of doing it just because it gives me that extra versatility of being able to just easily you know bring somebody into the mix drop them back out of the mix and so on so that's how i'm using it but i mentioned that i do have another little trick up my sleeve and that is that in addition to the three usb channels that we've got i'm also taking a fourth from the computer into the roadcaster and you could do this in a number of ways and probably the way that i'm doing it is not really the most efficient but i am in the early stages of this so what i've got here is this is basically taking usb it takes either a microphone or headphones and converts them to usb i actually use this when i'm on the road i use it for just plugging in a lav mic and headphones when i'm on zoom a zoom call when i want to get to a slightly better audio and i don't have a full setup with me so that's what this is for but basically all you need to know is i've basically taken the headphones the audio from the system and i'm taking that into the back into the into the roadcaster pro 2 at the back here so just using one of these trs cables and then it's into one of these to take up the side a bit size and that will then plug into one of these combo jacks at the back now what i will do is i'll get a the proper cable which will be a an xlr and then i'll run the xlr cable to go to the computer and then i'll have a xlr to trs trs been these little ones to take it down to that size and then i'll just plug this straight into the headphones of my computer the only reason i'm using this which is a bit of a workaround at the moment it's just because i literally don't have the cable to do this i do have some longer ones of these which i could in theory plug in but you tend to get a bit of an interference on those they're not the best cables to run any real length and certainly not for any sort of quality audio that won't go in and out so that's just my lack of cables i need to sort out my cable gain game but what this is effectively doing is this is now showing up as another device and i'm on my computer for my output so this is what i've got selected as my system speakers just the same as if i was plugged into the back of my mac mini with a cable i could just set you know set the output to headphones what this means though is i've got microphone i've got ecamm i've got skype and skype discord and i've got zoom too many communications and then there's this one here so if i just pop over to let's go over to epidemic play some random playlist and now you should not be hearing that however if i come back over here to this one again now we've got system audio and i can just introduce that into the mix and that should in theory be coming through onto onto the audio you can see obviously there it's bouncing for down and so now i've basically got complete control over all the audio over four different channels and so you can probably see how you might want to be able to use this i'm not suggesting that you go and replicate all of this it's really to just demonstrate the principles of it and the core thing to remember here is any communication apps that require two-way audio you need to make sure you've got mix minus switched on for those and then if you are using two different applications at the same time together that need to be able to talk with one another like ecome live with zoom or something like that and then just make sure that they have got their own dedicated channel you don't need to split out the system audio onto its its own channel you could just run the system audio onto any one of those channels and that would be that would be fine because it's only sort of one way i'm doing it this way just because i do want that extra control over the system audio separate to all of the other ones and so we have got those three channels but then yeah we have always got these other connectors at the back that we can utilize as well if we if we have the right cables that is i hope you found that useful i'll leave a link to some of my other roadcaster pro 2 videos over on the right hand side now see you in there


Good, let's start then. Thank you for giving me half an hour extra. Sorry. No, I'll try to finish in the hour. So there was a very good question over the break, and this was something I was trying to swipe under the rug, and that's a bad idea. These correlation functions of what should I say? So in principle, the scaling dimensions of an operator in the car algebra, so this scaling dimension that you get after the twist, the way I gave it to you doesn't need to be an integer or a half integer. And that would mean that correlation if that's the case, that would mean that the correlation functions of the twisted shure operators, twisted translated shure operators, would have complicated branch cuts and not be single valued. This would be counterintuitive because these are just twisted correlation functions of four-dimensional theories where they are nice and single valued. So indeed, you can check explicitly by just going over the list of shure operators that such branch cuts don't happen. So the OPE in the car algebra, which is the twisted version of the four-dimensional OPE, is single valued. And so you don't get complicated branch cuts in the correlation functions of the car algebra operators. So now you have a structure that you can associate to every four-dimensional n equals 2 theories, namely that of a car algebra, a set of correlation functions that's completely miramorphic. And now you can basically ask two types of questions, the first one being, well, if you give me a theory, then what is the associated car algebra? What are the generators from which I can construct everything else? And what is their singular OPE? So this is one question. And you can answer this for a variety of questions. And we've tried to answer it at least for a variety of theories. We've tried to answer it in some sense. And so that's the first half of this lecture. That topic will be covered in the first half. And then you can ask a different question, which is sort of what is the space of all car algebra that come from a four-dimensional n equals 2 theories? And are there sort of lessons I can learn about four-dimensional n equals 2 theories that hold in full generality without referring to a specific theory that follow from this car algebra structure? So answering that question, or at least giving you an idea of what kind of lessons you can draw from just the existence of a car algebra will be the topic of the second half of the talk. So for the first half, car algebra, I already gave you one theory whose car algebra I wrote down. I wrote down its generators. And I wrote down the singular OPE. And that's it. And that theory was just a free hyper-multiple. The next thing to do is, of course, the theory of the car algebra of the free vector multiplet. And from that, we can build, hopefully, in some sense, the car algebra of gauge theories. So the first thing we should discuss is what are car algebra for gauge theories? And how does all of that work? So first of all, I need to give you the car algebra of the free vector multiplet. So the free vector multiplet sits in one of these representations that I discussed in some abstractly in a previous lecture. It sits in an epsilon 1, 0, 0, and an epsilon bar 1, 0, 0 complex conjugate. So that's the name of the free vector multiplet representation. I forgot what the modern way is referring to this representation. It's super conformal primary. It's phi, the same phi that Zohar wrote down in the previous lecture, which is just the scalar. If there's a non-privile non-abiding gauge algebra, it sits in the adjoint. Then, of course, I can act with a supercharge. I get a gegino. And here, I get the self-dual part or anti-self-dual part of the field strength. So this would be, I think, the epsilon multiplet. And the epsilon bar just points the other way and has the conjugate of everything. So which one is sure? There is a sure operator in this multiplet, which is good for us. This one is not because it is an asymmetry singlet. This one is also not because it's an asymmetry singlet. And in fact, this is the sure operator. So it's a gegino. It has j1 equals, in my case, j2 equals a half, j1 equals 0, r equals a half, and delta equals 3 halves. So I think that would give me a sure operator. And so this guy is sure with dimension h, which is delta plus j over 2. So that's one. So what kind of operator do we get? Well, if I define b of z to be the usual thing, which one do I take here? lambda tilde plus of zz bar in the q-columnology and the same z lambda i plus dot. Oh, here's a dot. Here's no dot, zz bar q-columnology. And this guy, I'm going to call not c, but del c of z. Then the OPE of these guys is 1 over z minus w, which just follows from the free theory. So computing the OPE is trivial. And the Kyra algebra is generated b del c with this OPE. So if I say del c, I can do this. But then I cannot really talk about c. And if you think about the multi-composition, like you do to get, for example, from the stress tensor self-OPE to the VeraZera algebra, what you see here is that the zero mode of c is not present in the Kyra algebra. So in fact, this space of states includes all the modes of b, all the modes of c, except the zero mode of c. So what I'm going to do is I'm going to say the Kyra algebra is generated by b and c, except the zero mode. And I'll add the little caveats to the equations that are to follow. But unless you force me to, I was not planning on explaining this any further. The details are in our paper. It's a small subtlety. So it's kind of a technicality. And for that reason, I don't think it's particularly conceptually very important for what I'm about to discuss. So this is a bit of a silly choice. I should have just called this something like d, right? And then we would have a bd. And then it would all be fine. And then I wouldn't have to talk about this zero mode. But this silly choice will be useful for what follows. And that's why I'm doing this. So now let's talk about non-trivial gauge theories. We're going to be nice and abstract. So let's not commit to any specific theory. So we're going to define a general gauge theory, t gauge as three vectors, well, as vectors, vector multiplets in the adjoint of some gauge algebra. Don't need to write that down. G coupled to, well, in principle, if you have a Lagrangian theory, this would be hypermultiplets. But of course, I can take some crazy non-Lagrangian theories. And all I require here is it for this symmetry to be gaugeable at this level is that it has a global symmetry g that I can gauge. So I'll take a general t with global symmetry g. For example, a bunch of free hypers would do the job often. But I could take another theory. And then I couple them in the usual way. I gauge the symmetry. And then, of course, I compute the one loop beta function. And if I want this to be a super conformal field theory, then I require that the beta function vanishes at one loop, and by n equals 2 super symmetry, that's sufficient for complete conformality. And the one loop beta function vanishing is the same as saying that the level of the flavor central charge of this theory, k4d, is equal to 4 times the dual coccitor number. So fairly abstract, but I hope it's clear what we're doing here, right? So a question, natural question to ask now. If you give me not this theory t, but just its chiral algebra, and you give me a bunch of vectors in the adjoint, well, instead of the full vector multiplet, if you give me the algebra associated, the chiral algebra associated to these vector multiplets, can I do the gauging purely at the level of the algebra? Is there some operation that I can do if you just give me these two chiral algebras that gives me the chiral algebra of the gauged theory? So for example, the chiral algebra here has gauged non-singlets, right? In principle, I don't have to. So in principle here, there are operators charged under g, and same here. And of course, in the end, I want to only have gauged shinglets in the chiral algebra. So what's the operation? Is there an operation that I can do that sort of combines these two chiral algebras in some non-trivial way and gives me the chiral algebra of the gauged theory? And the answer to this question is yes. And it's a very nice prescription. So let me use this notation to say the chiral algebra of TG from the chiral algebra of T, which in particular contains a g-affin-cos-moody current at level k2d equals minus 2 times to do a coaxial number. So in particular, so what I'm saying here is just that this chiral algebra of this original theory contains some current, ga of z, where is an adjoint index of the free vector multiplets. Whoops, the kind of algebra of the free vector multiplets. We know it's generated by BACA, modulo of the zero amount. And the way to do this, so the prescription is as follows, I'll define it's a BRST called homology prescription. So you define the BRST charge as the integral dz over 2 pi i of the BRST current, JBRST of z. So this counter integral, if you act with the charge on a given operator, you take this counter integral around the operator. And all it does, of course, is just pick out the simple pole in the OPE of this BRST current with the operator. So alternatively, you can just look at the OPE, take out the singular, the simple pole in the OPE, and that's what the action of the BRST operator is. Where JBRST is the usual one. So we see. Well, here it's fine. And the claim is now that the carrier algebra of the gauge theory is the BRST called homology. So it's, again, a homological problem. We're already in the homology of funny cube, but now we do a BRST homology in the carrier algebra. So it's a BRST homology over the space of states that are either in chi t or the carrier algebra of the three vectors. And this is true. Margello the zero mode issue. Oh, sorry. The Margello has to go outside. So this is important. So I say BRST homology, but everyone to take the homology of this guy, I better check that it's no potent. So I have to do something like this. QBRST on anything is 0. And indeed, this is true. So note that this is true only if. So there's a current here which has a non-trivial OPE, but itself OPE is determined, the singular term is determined in terms of this level. And only if k4d is equal to 4 times the dual cox to the number of g. So if the Monlou beta function vanishes, then I can do this, play this game. And if not, I cannot. So this is the claim. I'm not going to do this in very much detail, but as a first. So a zero order consistency check that you can do is check that if an operator is BRST closed, then it's automatically gage invariant. This is a true fact of life that I wasn't going to explain. But at the very least, restricting yourself to the QBIRST closed guys indeed kills all the non-gage invariant states. In fact, that one property may be something I can actually show. So how am I doing? Yeah, I think I have time to do that. So let me do the example of a charged operator, or i of z, in the Chiara algebra. So we have this Chiara algebra, as I said, contains an affrancatsmoody algebra. It may be much bigger. It may contain all kinds of charged operators. Let me just take one of these operators and check that it's not BRST closed. The OPE of a charged operator, basically, by word identities, has to take this form. So it can have more singular terms. It can have more regular terms, but this is the OPE of the current with any charged operator, where this is, of course, the associated representation matrices. So now it's easy, because the action of the BRST operator this guy, well, let me insert it at the origin for simplicity, is just a simple poll on this OPE. So there is some CA. But CA comes from another sector. It comes from the free vector multiplet. So the OPE of c with this guy and b is automatically regular, because these sectors don't talk to each other. So I have CA, A, G, A minus 1 half, and then FABC, CA, where did I put the C, CB, BC. And the only thing that's going to give me a simple poll is precisely this OPE. So this is CA of 0 TA. And that's it. So here, you see some non-trivial composite operator. It's the normal-ordered product of these two guys, but it's certainly not 0. So this is not BRST closed. Lambda becomes B or C. And so once you can do it as an exercise, try to see that your B and C operators are also not too close. So here, it was important that I took a charged operator that was in the kera-algebra of T and not in the other kera-algebra, the kera-algebra of the free vector, but you can easily show that the free, the keginos also disappear. And so in the paper, we have a bit more explanation than I have time to give. In particular, we can think of this BRST operator as being something like a one-loop correction, morally speaking, at least, to our funny supercharge. So we're in the homology of funny queue. And now we're going, in that homology, restrict to a further homology. And in some sense, this is just a one-loop correction to the supercharge that you would get if you would properly define it in the interacting theory. We also have a claim that this is enough, that this one-loop correction, just like the beta function, if you check it at one loop that it vanishes, it vanishes completely. Our claim is, we have a similar claim that this one-loop correction, this BRST game, is indeed enough to get the kera-algebra of the interacting theory. Correction in the sense of bijection? If you want, yes. It's the one-loop correction. Yeah, I don't have an explicit check of that, but it's really the one-loop correction that you would get if you would write down the interacting Lagrangian and properly determine the associated Q and S out of which our funny queue is made. So this is a nice trick that allows you to, in some sense, quickly determine the kera-algebra of gauge theories. Maybe I should jump ahead a little bit to change my order a little bit from what I wrote down. So I kept one thing of Zohar's notes, of Zohar's lectures. Let's look at this theory, SUN with two n-hypers in the fundamental. And let me take n greater than 3, because for n equals 2, the flavor symmetry gets enhanced. n equals 2, the flavor symmetry gets enhanced to SOH, and that enhancement gives you a more fun kera-algebra, but not something I want to talk about in detail now. So what are your, what operators survive this BRST game and are part of the kera-algebra? Well, they have to be gauge invariants. So first of all, let's write down what we have in the un-gauge theory. So in the un-gauge theory, or the free theory, we would have free-hypers. We have q and q tilde. And these, of course, have our symmetry indices as usual. They have flavor indices, A, A, and they have gauge indices, I, I. And actually, I'll do it the other way around. So this will be flavor, and this will be gauge. So this gives rise to a pair of simplectics bosons we've seen before for each A and I, q tilde, A, I. And then there is the free vector. So we have to get genus, and those give rise to your BC system. And out of this, we have to build gauge invariant combinations. And not only gauge invariant combinations, we need to build combinations such that they are BRST closed. And in fact, there's a very nice, there's a very natural thing you can do, which is just this. So you take q, where did I put the indices, q, A, I. So this is no tilde, q, A. So just take the two hypers and you contract their gauge indices. And if you symmetrize this, so you get an operator of dimension two, which is a triplet of the r symmetry. So this is the super conformal primary of a B hat one multiplet that I discussed before. And in the Kyra algebra, so this gives rise. So this is in the B hat one multiplet. And in the Kyra algebra, this is of course the same thing as q, A, J, q, A, I, which I define to be some dimension one operator. So remember that these were dimension one half, q, q tilde were dimension one half. And so this is a dimension one operator in the Kyra algebra. And this is precisely my flavor symmetry current. So now you can see this sort of in two ways. You can view this flavor symmetry current as coming from a B hat one multiplet, which you had in that theory, or you can see it as just normal ordering the elementary building blocks in the theory. And in fact, you can split it into a trace.  You can check that this is an U one. I think I wrote down the level somewhere. Yeah, so this one doesn't really have a level because the normalization is ambiguous because there are no structure constant to normalize the thing by. But this one has a level, but you can easily determine because you know the OPE of the elementary building blocks. So you can just take the OPE of this current with itself and you find that it has minus Nc. So here, sorry, I work in conventions where this is Nc and two Nc. This is equal to Nf. So this is how you can sort of start building your Kyra algebra. You have the engaged non-invariant building blocks. You combine them in a gauge invariant way. And then of course you check that it's BRST closed and not BRST exact. And then you get operators in the gauge theory. So these are simple ones. There's of course also the C hat 0, 0, 0, the stress tensor multiplet, there's the SU2R symmetry current that we already saw before, Ij. So in the 4D theory upstairs, it's some complicated combination. In the Kyra algebra, it looks a bit simpler. It looks like this in terms of the elementary building blocks. Q, let me not contract all the indices. They're contracted in the obvious way, minus lambda, minus b dash c. So this, you can check that this particular combination is actually in the columnology of Q, BRST. And it's sort of precisely what you would get if you would take the four-dimensional expression for the SU2R symmetry current and do the twist. Because if you take the SU2R symmetry current, you basically see all the fields that are charged under SU2R and in the free hyper, it's precisely this and in the free vector, it's precisely this. And you don't see the gauge field, you don't see the scalar dimension one scalar in the vector multiplet that you don't see the fermions in the vector multiplet because they're not charged under the SU2R symmetry. So there's a funny thing happening here which I'd like to point out, which is that if you have a flavor symmetry current, I can always define the so-called Sugavara stress tensor, T-Sugavara, which acts, this guy acts as a stress tensor on the currents, but it may not act as a stress tensor in everything else. So the Sugavara stress tensor is just some dimension two operator in the Kyberaw algebra, which I can build from if I have currents. And this is a proper thing I can always do. As it happens, in this case, T of Z minus the Sugavara stress tensor of Z. So in the original Kyberaw algebra, there are certainly two different operators. You can just look at how they're constructed. This T of Z is built out of Q's, Q tilde's, B's, and C's, whereas this J is built out of two Q's, so this guy is built out of four Q's. So these are different-looking operators. And in principle, they're different in the Kyberaw algebra. However, if you take their difference, then you find that this is Brst exact. And so in the gauge Kyberaw algebra, these two operators become the same. So well, now we have to make some conjecture as to what the full Kyberaw algebra of this theory is. So we have some generators that we knew about. We know that, well, there's these currents. Then we thought maybe the stress tensor is a new generator, because I cannot build it as a normal-ordered product of currents. But that's false, because the stress tensor is actually the same in the gauge theory as a normal-ordered product of currents. So we don't have that as an extra generator. And so maybe we're done. Maybe this is just the full Kyberaw algebra, right? So I'm not going to write the current self OP again. We've seen it before. So I can just claim, well, maybe these currents generate the Kyberaw algebra, and their self OP is the canonical one for an FI cut smoothie current. Is this true? This is a tough question at this level. Are there natural other gauge invariant operators that I can build out of, let's say, the hyper multiplets? Sorry? Variants. Thank you. And it turns out that these are new generators. So we have new generators. These turn out to be generators, which are q, q, and then some epsilon to contract all the gauge indices. So where did I put my gauge indices? A1, An, A1, An, and then I1, In. So they're in the enfold anti-symmetric representation of the flavor index. And in the Kyberaw algebra, I just make the big q's, little q's. Sorry, I should have done that right away. And this defines some baryon operator. So in the ungauge theory, this was not a generator. Because in the ungauge theory, I had the q's to play with. And if the q's are generators, then I can just build this guy out of q's. But in the gauge theory, the q's have disappeared. They're no longer in the columnology. And so I need to add these guys to the Kyberaw algebra. There's new generators. And so in this way, the game of determining what your generators are becomes very non-trivial. And of course, there's also b tilde. From gauge theory, I'm going to switch to q. From a 2D point of view, you could actually not have guessed that. Because there is no need. This algebra, which was just the u1 plus SUNF afrenkatz moody symmetry, closes on itself. So it's a consistent subsector, as it happens, of the full Kyberaw algebra of this theory. And so there was no way, if someone would give you this, there was no way to check that it was inconsistent as a Kyberaw algebra. But that's not what we're asking. What we're asking is, what's the full Kyberaw algebra of this theory? And then we have to deal with these kind of issues. So our conjecture is that this is it. So we have the Kyberaw algebra generated by this guy and the Kyberaw algebra. And then the two baryons, it's baryonic type operators as additional generators. And our conjecture is that's it. So this is beautifully stated in the grandian description, but you want to go beyond, right? I want to go beyond. Yes. Are you saying I don't have time to go beyond? No, no. I am asking how you know if there are baryons or more crazy things beyond? Oh, if you, OK, let's ask about beyond Lagrangian a little bit later. So for Lagrangian theories, now this conjecture stands and it's not proven. In fact, even for Lagrangian theories, as soon as they're noninteracting, this BRST problem becomes non-trivial. And we have no proof for the full Kyberaw algebra of any Lagrangian theory. Even here, the simplest Lagrangian theory you can write down, basically, we don't have a proof that this is the full set of operators in the BRST homology of the Kyberaw algebra that started with these gauge non-invariant fields. So this is purely a Kyberaw algebra problem at this level. It's just a BRST homology problem. And we were not able to solve it. No, the bootstrap analysis, you can do small things. Like you can try to take a self-OP of this guy with itself. And maybe you see some crazy object that you could not generate in any other way. Then that would mean, well, you add this object to it. But at some point, we often find this, we check that this doesn't happen. And that sort of the Jacobi's are satisfied. So this is, again, a nice close subalgebra. But are there other generators? I don't know. In fact, we don't even know if, for any theory, we don't know for sure if the Kyberaw algebra is finitely generated. Could have infinitely many generators. I don't believe that to be true. I strongly believe that they are finitely generated. But they don't have a proof for it. And you see how complicated the question of generators becomes in this BRST homology problem. You throw away some stuff. And so suddenly further down, there could be things that were not generators before that suddenly become generators. Sorry? What kind of Kyberaw algebra does the value of the generator? I don't think the Kyberaw algebras, the question is what Kyberaw algebra do the variants generate. And they cannot be viewed independently from the currents as it happens. Because in the self-OPE of the variant, anti-variant, you will find the currents back. So this does not close on itself as a Kyberaw algebra. So it's just some extra sector that needs this Kyberaw algebra. I lost my board. Gravity seems to work in mysterious ways here. So what should I say? I should say a few things very quickly in words. One thing I want to say is if you want to check these kind of conjectures, you can sort of go over the list of all the operators that you can build at low orders. You just build all the operators that you can from these building blocks. And you'd solve your BRST problem order by order in this dimension. And then for the first few levels, you find no new generators. And you count yourself lucky you think, OK, maybe my conjecture is true. Then in principle, there's another thing that you can do, which is compute the super conformal index. There's a particular limit of the super conformal index, the so-called SURE limit. So this is essentially the S3 cross S1 partition function, supersymmetric partition function, which in a particular limit just counts to SURE operators. This is a happy coincidence. It counts them with signs. So it becomes almost a character of the Kyberaw algebra, except there's a minus 1 to the f. So it's a graded character of the Kyberaw algebra that you get from the SURE limit of the super conformal index. And the Kyberaw algebra itself has no supersymmetry. So I can't say that this is the index of a Kyberaw algebra. That's a meaningless term at this point. So it's just a graded character of the Kyberaw algebra. And so you can, for example, if you have a conjecture for a Kyberaw algebra, you can compute its graded character and see that it matches, whether it matches or not, the super conformal index of the four-dimensional theory. This gives you some evidence, but not full evidence, because there could be cancellations. You don't know the exact structure of nulls, et cetera. But it would help you a lot. Unfortunately, as it happens, computing the super conformal index for these theories is relatively easy. Computing just for this Kyberaw algebra, computing for this guy with these generators, computing the graded character, or the character of this thing, is very difficult. That's because these are affine currents at negative level, for which the usual cuts formalized for the character don't work. And so basically, we can do this only level by level. And so we can go down to level six or seven, and then our mathematical code gives up. And so that's the order to which we check these conjectures. So there's an indexology section that I will completely skip. I can say much more about the connections to the index, the various limits, et cetera, et cetera. But I want to get to other stuff. So let me focus on that instead. So before I end this section on Lagrangian theories or specific theories, I want to add some conjectures for Kyberaw algebra of specific theories. All of these are conjectures. So nf equals 2nc, super conformal QCD. That's the one we just discussed. So it's SU nf plus U1 at level minus n affine cuts moody symmetry. So that's the current part plus variance with OPEs that you can find in our paper, or at least some case. For similarly, there's a nice so-called Minahan-Nemeshansky theory. So let's look at the E6 theory. This theory is a bit obscure. It's not Lagrangian. So there's no gauge theory description like this. But the index is known. And we know that it has E6 flavor symmetry. And so at the very least, it has E6 affine cuts moody symmetry. And as it happens, the level turns out to be minus 3. So we also know that about the theory. Our conjecture is that this is all there is. There is no other generator in the Kavara algebra. This is not trivial. We checked it again against the index. But otherwise, we can check it, because it's just some abstract theory that we don't know very little about. So let me also say that if your theory has extra supersymmetry, for example, n equals 4 super young mills. What do you mean by n equals 4 super young mills? Those I don't know. I'm not so sure about that. For sure, contain this. But I'm not sure if that's the entire Kavara algebra. n equals 4 super young mills. So the Kavara algebra of n equals 4 super young mills, let me just say this, has 0,4 Susie. Well, it's Kavara, so I can just say it as n equals 4 super super young mills. And I should add the qualifier if you want to be precise that this is small n equals 4. So this just happens because you have extra supercharges floating around in the four-dimensional theory that to revive the twist, and they become super, or super currents, they become super currents in the Kavara algebra also. And the Kavara algebra of n equals 3 theories has n equals 2 supersymmetry. And I should say that these are super VRZera algebra. So just like the flavor symmetry gets enhanced to this infinite-dimensional Katsumudi algebra, these supersymmetries get enhanced to infinite-dimensional super VRZera algebras. So we have some conjectures for these Kavara algebras. But in the interest of time, I was not planning to discuss them. And so you can, of course, continue this list forever. And for all your favorite theories, you can try to determine what the Kavara algebra is. Try to solve the cosmology problem, or try to find it in some different ways. I think that would be interesting. What would be extremely interesting would be to try and see if you can, at least in one or two cases, solve this cosmological problem and have a conclusive proof for the Kavara algebra of the corresponding theory. OK. Any questions about Kavara algebras of specific theories or other questions you've had? So what's TN? TN is very nice. It has, of course, the three flavor symmetries. And those sit at, actually, the critical level. Because remember to gauge a theory, I need k2d equals minus 2h. But I gauge two TNs together, or two punctures together. And so for TN, it's minus the dual-coxater number, which is a very nice level to be at for a flavor symmetry. In particular, the Sugovara stress tensor, if you know what that is, it becomes a null state. Oh, I just introduced it, so you know what it is. It becomes null in itself. So in these three Afan-Kazmoudi algebras, there is no Sugovara stress tensor. But of course, the full TN theory has a stress tensor still. And then we believe there are some other generators floating around. This is not the full thing. But we don't have a good. We have some ideas about it. But we don't have, like for the others, we don't have a proof. Yeah, and then, of course, you can close punctures. And that's another beautiful procedure. Gaging was beautiful in the sense that you can do it purely at the level of the Kera algebra. If you know about the N theories, you also know that you can close punctures. This corresponds, you can also do this purely at the level of the Kera algebra. It's a procedure called Drinfeld-Sokolov reduction. And it's also be a risky problem. But it has to kill some of the flavors in it. For general class S theory, that's a huge class to us. I mean, we're just like simple gauge theories. We don't know. So for general class S, there's, of course, now a picture, which I can sketch, which is just you gauge and you close punctures and you do Drinfeld-Sokolov reduction. But for general class S theory, it's, yeah. It depends on the puncture, depends on the puncture. It depends on? It depends on the puncture composition. Yes. Oh, that's nice. So you want to ask if this is S2 or manifestly. That's correct. Gaging depends on the puncture composition. And it's non-trivial that if you take two different puncture compositions, you get the same Kera algebra. So this, in some sense, you could hope, would be some kind of bootstrap for Kera algebras, right? I take the Kera algebra of Tn and I glue it together in two different ways. And then I should get the same Kera algebra. So is there some constraints on the original Kera algebra that they can find in this way? I don't know the answer to that question, but I think it's fascinating. It would be very nice if you can actually get somewhere there. I should also say that basically the reason, when I claim that this PRSK problem sort of solves the whole thing, it also means there's no further coupling dependence. So you can actually show that all the three-point functions in a gauge theory are independent of the coupling. So all of this is sort of fixed by free theory OPs. There's no further coupling dependence. OK, I'm running out of time, but I have 10 minutes for two pages, which is going to be great. Let's do non Lagrangian theories just so that I can show you that there are certain bonds you can get, certain uniterity bonds that follow from this Kera algebra story. So let me take a theory T and let me suppose that it has flavor symmetry, flavor symmetry algebra G. Then if T is a good theory, there is an associated current. And in the Kera algebra, we have delta AB plus I of ABC, FC of JC of 0 divided by Z. Of course, if it's a good theory, then it also has a stress tensor. And if the theory has a stress tensor, then let me remind you it has an SE2R symmetry current in the same supermic conformal multiple. And that guy gives me a stress tensor in the Kera algebra, so with the usual OPE. And finally, if this guy is a good stress tensor, which we'll assume, then the stress tensor OPE with this current is, looks like this. Oh, this is it. So this just, you can either compute it upstairs or just follow us from the fact that this is a stress tensor and this guy is a free or zero primary. The fact that it's a free or zero primary follows because there can be nothing of even lower dimension. So this is a consistent subalgebra. The OPE closes here. So in principle, this is all perfectly good. And it, of course, determines all the JT correlators. So this determines the TJ correlators. And also the correlation functions of their normal order products. So for example, you don't need to copy this, but I am going to need it a bit later. So this is in our paper also. Let me take a four point function. And let me move the four points to the canonical positions, point one at the origin, point two at some coordinate z, point three at one, and point four at infinity. And then this has to, as z goes to zero, it has prescribed singularities. As z goes to one, it has prescribed singularities. And as z goes to infinity, it also has prescribed singularities. So these singularities come from this. And so you can just solve this. It's easier to do in Mathematica, but what you get is something that looks like this. z squared over 1 minus z squared delta AD delta BC. So these sort of take into account the three strongest singularities as you go to 0, 1, and infinity. And then there are some subleading singularities, k2d z minus 1. So this four point function is just fixed. It follows directly from this simple equation. So now let me look at a particular operator. Let me call it j squared of z. And I define it to be jA, the normal ordered product of jA of z, jA of 0. So in other words, it's just the limit as w goes to z of jA w jA of z minus the singular terms, k2d over z squared times delta AA, which is just a dimension of g. And that's it. The subleading term here, this is also, in principle, a singular term. But of course, by the anti-symmetry of the structure constants, it vanishes if I contract the indices in this particular way. So this is how I define the operator. And this should be w minus it. So what is this operator? It's some operator in the Kaira algebra. Where does it come from? It's a dimension two singlet. So it's basically our Sugavara guy. But where does it come from in four dimension? It could be the stress tensor. It could be the same operator as the stress tensor here. And then it would come from a C hat multiplet, a C hat 0, 0 multiplet. There's another option. If you just go over the list of possible multiplets and you have to, and you see what this j squared of z could be, given also the fact that it appears in the OPE of j with itself, it can be C hat 0, 0 or a B hat 2 multiplet. And that's about it. I think it can also be a higher spin current, but let's assume our theory doesn't have higher spin symmetry. And then it can be either this or that or a combination of these two, so linear combination. What I'm interested in is the B hat 2 part of this linear combination. In general, this guy will be a linear combination of the two. And I'm interested in the B hat 2 part of the guy. So how do I extract it? Well, a B hat 2 will have 0 two point function with the C hat 0, because these are different types of operators. And the C hat 0 I know, because the C hat 0 is just a stress tensor. So I'm going to make sure I'm going to add to this j squared a multiple of the stress tensor so that it's orthogonal to the stress tensor itself. Are we good? So let's write all the norms, or in this case, two point functions for all the operators we're considering. So these are the dimension two operators. t z t 0 is this. t z, sorry, t z j squared of 0. Well, that's just the limit as that goes to w, or as that w goes to 0, in this case, of t of z, j a of w, j a of 0. And this three point function I can compute from the OP of t with itself, with j. So it's a limit as w goes to 0 of, well, let me do this schematically. So j a of w times j a of 0 over z squared plus del j a over z plus dot, dot, dot. And then plus the other one where you swap w with 0. And then you can use the fact that by cluster decomposition, this guy should go to 0 as z goes to infinity. So this vanished by, in the total sum, these will vanish by cluster decomposition, because this is just a dimension two operator. So I only need to look at the singular terms. The singular terms are a little bit non-trivial to work out. So you get some funny cancellations. But in the end, you find that this is something which I have, I do have it. It's k 2d times the dimension of g. That comes from the two-point function of jj, contracted with itself over z to the fourth also. And then, of course, there's j squared of 0 with itself. But that is very simple if I realize that that's just a limit of that four-point function. It's the z to 0 limit with all the singular terms subtracted. So this is immediately computable. I don't have time to do it exactly. But I think it's 2 times k 2d times the dimension of g again. Did I do this correctly? Yeah. Dimension of g times k 2d plus the dual-coxeter number. Where the dual-coxeter number is something like f abc, f abc, up to factors that I forgot. But it's something like that. So you see, my two-point function j squared is not orthogonal to the stress tensor. My operator j squared is not orthogonal to the stress tensor because this two-point function is 0. So we're going to define the new guy, j hat of z. And I want it to be orthogonal to the stress tensor. So to do that, I'll take it to be j squared of z minus whatever this thing is. So it's 2k 2d dimension over c times t. So this, I claim, has to be a b hat 2 because t is by construction the c hat 0 is 0. And you also have to check that it is not a descendant. But in this case, you can show that it's a primary. And so it has to come from a b hat 2. So j hat of z is a twisted b hat 2 operator. B hat 2, a twisted b hat 2, well, so more precise. I mean, let me write operator and say in words what I precisely mean. What I precisely mean is you take the sure operator in this super conformal multiplet, which happens to be the super conformal primary. It's the guy at the top. And it's the twisted translated version of that particular operator. And I can compute that j hat z t of 0 is indeed 0 if I pick my factors of 2 and other case and so on correctly. But more interestingly, you will find that j hat z j hat 0 is what? It is 1 over z to the fourth. Now times some funky combination of terms, which I believe is 2k d, where d is the dimension of d, times k 2d plus the do a coccidum number, minus k 2d. This is also k 2d. So this tells me that the norm of this b hat 2 guy is fixed in terms of these sort of canonical numbers in the Chiara algebra. So if you give me the level k and the type of algebra, so I know it's do a coccidum number and dimension, and you also give me the two dimensional, the flavor central charge, or sorry, if you also give me a C central charge, then I just know the norm of this guy. But this is just a norm of a b hat 2 multiplet. It's just a two point function of a b hat 2 multiplet twisted. And in the Chiara algebra, the norm may be positive or negative. But the b hat 2 multiplet upstairs must have a positive norm. That's a unitary theory. So this should also be something like epsilon, but it's a b hat 2. So let me call it m. It's in the 2. So it has 4 r symmetry indices of z z bar u i to u l.   But some norm. And in conventions that I'm not entirely sure about, but I think it's these conventions, n has to be positive. So unitarity tells me that this is a positive norm. Maybe it's negative. I'm not entirely sure about the science now. But I think with these choice of epsilon's, you basically have to go to a basis where everything is orthogonal. So you have some orthonormal basis. And then you check that the coefficient is indeed positive. But this norm I've computed in terms of the elementary quantities of the theory. And what this tells you is that there is some non-trivial inequality on these coefficients that has to be obeyed in any sort of unitary theory. So sir, you showed that this combination is positive, but is it expected to or? It's not. It's not. Oh, you just find it. So you kind of predicted it to be half-multiple. Does it guarantee that this is positive or? No. So what this leads to is the following constraint. It tells me that if I translate this back to 40 language, remember that c2d is minus 12 times c4d. And k2d is minus c4d over 2. Then I get, if I did this correctly, that there's this inequality over k4d minus 12. And this has to be true in a unitary theory. And it's a non-trivial consequence of the Chiara algebra. In fact, we checked that all the theories that we know, for a large class of theories, we checked, of course, that this thing is inequalities obeyed. We know what happens if it's saturated. If it's saturated, we know that the stress tensor there becomes equal to j squared. So there's a null state in this set of two operators. So j squared minus the stress tensor becomes null when this thing is saturated, which precisely says that the stress tensor, that j squared and t are the same thing, basically. So in other words, the stress tensor of the Chiara algebra is the Sugavara stress tensor. So yes. Yes, OK. The question is if I could, sorry, if you don't know the Chiara algebra, if you don't know the Chiara algebra, the question was if you can find this unitary bound just directly in four dimensions. I am not sure if what it would amount to is, you give me a 40 theory.  And I would need to know the two point function of the b hat 2 in terms of if, like all I give you is the two point function of the b hat 1's or the four point, not even the four point function, right? I give you the two point function of the b hat 1's and I give you the central charge. And now you have to tell me what the two point function is of the b hat 2 because that is the thing I determined in terms of k and c from the Chiara algebra. No, I used the Chiara algebra to compute the norm of a b hat 2 multiplet, which I could not have done otherwise. Because I computed this j squared two point function from the four point function of single j's by taking the particular limit, right? So I had this four point function which determines the norm of a j squared. It determined this thing. And I don't think I would have been able to determine it otherwise. That's a non-trivial two point function. This thing required crossing symmetry and all of these things to be obeyed and required the mere morphicity. It's not just a short distance thing. So I don't think I would be able to get this number without knowing this. And that's why I needed the Chiara algebra. So we know when it's saturated, that's what I wanted to say. If T sub gavara equals T, so basically this b hat 2 gets zero norm. It decouples. So there is no, in the physical theory, there is no b hat 2 in the singlet in this sector. So only, of course, this is just a subsector. These were just the subsector generated by these guys. And in this sector, there is no b hat 2 in the flavor singlet combination. This b hat 2 disappears. And the suga-vara stress tensor becomes the actual stress tensor. So this also translates, by the way, into some Higgs-Brenge-Karow-Ring relation, which we, yeah, is then a consequence also of the saturation of this equality. So in this case, you get inequality that involves flavor central charge and central charges. More generally, other people have derived bonds like this one, C40 greater than 11 over 30, and other bounds on flavor central charges that don't involve the C central charge, but that depend on the particular algebra that you consider. So it's expressible in terms of some basic quantum, basic numbers in variance of the algebra that they didn't take notes, so I can't reproduce them right now. But they're also K40 inequalities of this type. So these inequalities, I believe, would not be possible to obtain them without knowing this Kyra algebra. But now that you know about Kyra algebras, you can derive them. And these, in some sense, constrain the space of all four-dimensional n equals 2 super conformal fields, both Lagrangian and non-Lagrangian. No matter what theory you have, if it's unitary, if it has a stress tensor, and in this case, if it has flavor, then these bonds that we have derived must be obeyed. So in this sense, this constraints the landscape a little bit further. I think our dream here would be to get even many more constraints, such that maybe in some sense, you can completely classify the space of four-dimensional n equals 2 theories, at least say with small number of generators for the Kyra algebra, just because they are the only consistent Kyra algebras that are compatible with four-dimensional unitary. This is, of course, a very far-fetched dream, but this is sort of a first step in the right direction, where you get at least some non-trivial constraints on the space of four-dimensional theories that hold in full generality. So that's why I think this is a nice result because of its universality. It doesn't need Lagrangian. It doesn't need anything, except 40 n equals 2 theories and basic assumptions there. So that's all I wanted to say about this. There are tons and tons of topics that I could have talked about and didn't. I didn't talk much about the index. I didn't talk much about sort of further ideas about unitarity bounds. I didn't talk about the Higgs branch much and the connection with the Higgs branch as a variety, how you can get this from the Kyra algebra. There's a beautiful story there. I didn't talk about defects. I didn't talk about connections with localization. I didn't talk about connections with holography. I didn't talk about partition functions with defects. And I think that's about the list of topics that people have already written papers on. I didn't talk about six-dimensions. I didn't talk about two-dimensions and et cetera, et cetera. So there are really tons and tons of things that I could have followed up on. But I think since I'm out of time, I'll just stop here. Thank you.


Speaking of progressing, Kent has our next quick tip for us. He says, I finally bought some air tags on a pre Black Friday sale. And before they arrived, I started questioning my choice. I wondered if both my wife and I would be able to track our tagged items together. My initial searches seemed to say, no, one air tag, one owner, so to speak. However, most of those articles I found were dated a year ago. That may have been the case before, but now with iOS 17, that has changed when the owner can designate one or more additional users up to five. They do not have to be in one's family group, but they do need to have an Apple ID. And it's true. Yeah, being able to share air tags really changes that the nature of how these things can work. I think it's I like it. I think it's great. That's awesome.