Howdy how's it going? My name's Davy Chappy and today it's time to ink some sweet tats and make a bunch of old people say You'll never get a job with those cuz we're gonna be talking about each of Eberron's magical dragon marked houses And their associated dragon marked tattoos I'm gonna go over who can get dragon marks, how they get them, what marks mean, and I'll be talking about the massive influence that each Dragon marked house has over the continent of Corvair and by extension the entire world as always keep in mind that a lot Of this is just my opinion So if you feel like I'm too much of a nerd who doesn't understand the true art of tattoos feel free to leave a comment down Below but with that other way let's begin so a dragon mark is a magical tattoo that acts as the physical representation of the will of the Three primordial dragons via an ancient prophecy that Ciber is foretold known as the draconic prophecy in layman's terms A dragon mark is a tell-tale sign that history has its eyes on you because these glow-in-the-dark birth marks grant an innate magical power To the bearer with the specific type of magic depending on which of the 13 dragon marks they have and the strength of the magic Depending on whether the dragon mark is a least lesser greater or even mythical Ciberous version of said dragon mark the 13 different dragon marks are passed down via 13 different bloodlines with only a specific race Able to bear each dragon mark and even then the chances of one appearing are rare and largely random each separate bloodline has formed a Dragon marked house and each house controls some form of service or trade in Corvair that corresponds with their marks power the 13 Different dragon marks along with their houses are very numerous and a bit confusing So you're gonna have to bear with me a second here because they are as follows the mark of making bore by the humans of House canith which runs the fabricator in tinker guilds and can use their mark to both mend and create items the mark of the Sentinel bore by the humans of house dineath which runs the defenders and blade marks guilds and can use their mark to gain protective spells the mark of Hospitality bore by the halflings of house galanda which runs the hostels guild and can use their mark to conveniently create food and lodgings for people The mark of healing bore by the halflings of house Dorosco Which runs the healers guild and can use their mark to I don't know maybe heal the mark of warding bore by the dwarves of house Cundurac, which runs the banking and warding guilds and can use their mark to warn you when there's a bitch incoming. The Mark of Storm, bore by the half elves of House Lyrandar, which runs the Raincaller and Windwright guilds and can use their mark to control the goddamn weather and slap people with the might of Zeus.  The Mark of Passage, bore by the humans of House Orion, which runs the courier and transportation guilds and can use their mark to walk through walls, disappear and fly. The Shadow, bore by the elves of House Feralyn, which runs the entertainers and artisans guild and can use their mark to cast scrying spells as well as illusions and other deceptive magics. Also, a challenger approaches in the form of House Therani, which is a splinter group that broke off from House Feralyn, making them bitter rival spy organizations. The Mark of Scribing, bore by the gnomes of House Sivis, which runs the speaker and notaries guilds and can use their mark to control words and writing, which I'm told is very useful. The Mark of Finding, a special dragon mark that is bore by the humans and half orcs of House Therash, which runs the finder's guild and can use its mark to find lost things such as runaway criminals, your TV remote and my will to live. The Mark of Handling, bore by the humans of House Vidalis, which runs the handlers guild and can use its mark to breed superior animals by checking their secret IV rating. And finally, the Mark of Death, bore by the elves of House Vole, which got itself caught in the middle of a civil war between the dragons and the elves and decided that the best solution would be to interbreed by creating the first elf dragon hybrids to show everyone that mutual peace was achievable. Both the elves and the dragons looked upon this horrid, elf-scaly, furry abomination and, to Vole's credit, they immediately made peace with each other.  Good job, House Vole. And let that be a lesson to you all, leave your weird slash fiction in your diaries where they belong or else you'll end up causing world peace between warring nations when they realize that it was their own hubris that birthed something so horrid and disturbing. But moving back to the dragon marks, there were some people early on that realized that their dragon marks didn't correspond with any of the known houses, or just any other mark in general, and this caused some discourse in the greater tattoo community. It seemed that these aberrant dragon marks were created when dragon-marked creatures of different houses procreated, with a child bearing a highly volatile mark that wildly varied in both magical ability and overall power. The aberrant mark also had a chance of manifesting on races that could normally bear a pure dragon mark, which led to a lot of awkward moments as commoners would celebrate getting their free ticket into the good life, only to be told, wait, nope, nope, wait a minute, yep, that's heresy. And subsequently being shunned by practically the entire world. The shunning actually went so far that, sometime between the banishment of the Dalkeer and the formation of Gallifair, all of the dragon-marked bearers waged a huge war of extermination on the aberrant dragon-marks. The war, aptly named the War of the Mark, is what inevitably solidified the houses as a presence in Corvair and pushed them to create a unified government unto themselves, ruled by a council known as the Twelve that would decide the rules and regulation for how dragon-marked individuals are to behave in life. And speaking of war and unification, the dragon-marked houses would see their greatest rise to power come to them, carried by a man named Gallifair. See, when the OG King Gallifair I was gathering all the countries to make his own super country, he enlisted the help of the dragon-marked houses to assist him in his goals. Of course, given the potential in growing their power exponentially and also the fact that Gallifair had a huge scary army, the choice was obvious. But King Gallifair wasn't a fool, and he knew that he had to create regulations for the houses so that they would never become too powerful and subsequently subjugate his people. So in return for letting them stay super rich and powerful, the dragon-marked houses were prevented from creating any formal army of their own. They were forbidden from claiming any land, and they could not marry into Gallifarian aristocracy. With these rules set in place, the Kingdom of Gallifair saw many generations of peace and prosperity alongside the dragon-marked houses. Of course, all that flew out the window when the last war started up.  In fact, at the end of the last war, feeling scorned and outcast by the rest of the magical birthmark community, the few remaining creatures with an aberrant dragon-mark said, screw you guys, and decided to create their own dragon-marked house with blackjack and hookers. They named this house House Tarkinon, set up shop in the city of Sharn, and threw rocks and insults at anybody who arrived at their gates. Now, with the Treaty of Thronehold established, the dragon-marked houses are in a very precarious place where they all seek to expand their power, but one wrong move will lead the world back into a full-scale war. But perhaps war is precisely what the Draconic prophecy calls for, and the bearers of the marks will lead Eperon into its true destiny. But that'll about do it. I hope you enjoyed this video. Leave a like and comment if you did. Subscribe if you want to be a cool dude, and maybe support me on Patreon so that I can slowly make my entire life revolve around D&D. Also, if you want to stay up to date in all of your Dabby news, I keep a link to my Discord and Twitter in the description below. But yeah, Dabby out.


You'll run into the need to read text or various files from your game's file system. Maybe it's a JSON file that configures things or a high score file from your player. Let's go ahead and make a really simple demo where I can show you how to do that. We've got a node 2D here. Just call it main. We'll save it as main. I'm in an empty Godot 4 project. We'll add a label. It's just a place to have some text and we'll add in the inspector just some placeholder text that shows what we're going to plan on targeting. We're going to load some text from a text file and display it in our Godot project. We'll run our game, make that our current, and you'll see placeholder text is here. All right, now let's set up our file. So we'll go to new. You can actually add a text file here in Godot and we'll call it greeting.txt and save it. You can open txt files in the Godot script editor. You can also open it in a different editor. But for us, we're just going to say, hello world, I'm from an external file. Go ahead and save that. Nothing's changed here. We haven't written any code yet. We'll attach a script to main and we'll just leave the defaults for now and click create. I'm going to go ahead and delete the process function and I'm going to clear out ready. I'm going to make this a bit bigger for ourselves. Clear out these comments. You might not see this void type signature. That's okay. I enable type signatures just so it's more clear, especially in screencasts, what the code is doing. Now we want to load our text from greeting.txt. So you can actually drag this into the script editor and you get this URL for our file which is kind of nice. We'll put that in a variable. We'll call it label text file. Let me make this bigger again so we can see it. So we've got our label text file. That's the path to it. Then what you can do is Godot has this file access API. You can call it .open. And then what you do is you pass in the resource. So label text file and then you pass in the permissions. So you can have read, you can have write, you can have write, you can have write, read. I don't know the difference between read, write and write, read. That's kind of funny. But if you wanted to write to a file, you would do .write. If you wanted to read from it, read. We're just reading. So we'll just set the proper flags there. That returns a file object, right? If we command click this and open it, we'll see that it returns a file access object. So we're going to go ahead and we'll just call that file. And let's actually take a second and let's rename this. So what I just did there is I double clicked this variable name and I pressed command D or control D. I'm on Linux or I'm on Mac. If you're on Windows or Linux, it'll be control. And you can then rename these both at once. Let's press the right arrow key. Let's actually rename this to res for resource because it's not a file. It's a resource. I think that makes it a little clearer. And then what you do, and we'll just say text is equal to file.get as text. Isn't that pretty nice? You can just get everything in the file as a text file. And we'll go ahead and we'll do print debug just to show what's in there. So click that, run the game because we want the ready to run again. And it says hello world, I'm from an external file. So in our code in a variable we have greeting dot txt in our code that we can do things with. So now we'll see remember we have label and you can just set the text property. You can just assign it our value text. Go ahead. I'm just going to run the game again because we want that ready loop to run again. And you can see we set the text in our game from an external file. Now this is pretty basic and I'm just showing you the foundation of what will be used for things like high scores, player config, save data. All this stuff right comes down to in the end.  You're opening it, you're reading from it, and then in the future we'll write to it and adjust with that. But for now, I just thought I'd show you how to do this really quick too. You want to run it in ready, right? If we did it in the process loop, it would happen every frame. We only want to do it once our scene is ready. And in your various nodes, maybe you'd attach a script and add to their ready callback. But for this case, we'll just do it here. And then let's go ahead and we'll just change this. And we'll say, and I'm a new line, save that, run the game again, and it's there. So that's pretty cool, and that's file access. Pretty simple, but an easy NGD script which I like. It's really great. It's easy to do. And you get cross-platform loading of those values. I hope that helps. Thank you very much for watching.


What's going on guys welcome to another video if you guys can tell by my voice.   There's something always going on, but I hope you guys enjoy this video We're gonna go ahead and head to the pond before I go.  This is actually pretty cool. Um, I Actually made this I like scan. I know you guys probably be interested in this, but I just want to show it You pretty much scan like this is not a picture. This is not from online. I actually did all this This is water right here. This is all water would die and also Photoshop But uh, yeah, I pretty much like scan this whole thing like this is like a picture that I took Like this is all the gushers and everything put on a scanner scanned it down with water and I had to get all those Spots perfect. I don't know.  I just saw my guy guys I've been pulled over Or I've not them. I've been pulled over many of times. I've got two tickets ever to two tickets and And both times I've been from the same guy in the same cop. I actually just passed them right there I'm a throw.  Yeah, that's what I got. Yeah, right here or two of them. Yeah, it's a good rod, dude For the price and everything dude. It's awesome. Yeah I'm something What that is? Oh my god, that's crazy. That's like recent too. Wow That's crazy that bird right there. Look at him. God, I think it's huge It's not turning out. It's pretty cold out here. It's just the wind and Sun just now came out So it's gonna defrost a little bit, but we have yet to even have a bite It's just when this weather gets like this it's noted in like 30 years here And so Savannah's already not used to getting that cold weather and then it got warm and then it got cold right again These fish are just probably Smashing the head.  It's all on the car. I can't wait till the weather is, you know, back Come out here and you know fish regularly and actually catch some fish without having to like break your back doing guys just got home not All right guys just got home Not too long ago When fishing is absolutely horrible with the weather it doesn't surprise me once so ever But we had that practice so that was the deal I want to see if I get some cool content, but those fish were just not gonna bite and We tried our best and that's what we could have done, but I'm making this video somewhat of a positive video in a way I have something I do want to add in Anyways after we went fishing You know Isaac went and ate and now I'm back here and I laid down and I just feel I was feeling fine when I was fishing And then when I ate I felt like fine. I mean I still felt I didn't feel like good, but I felt fine Now I'm just feeling horrible. Like I said down earlier I just feel horrible. I don't know if I'm gonna be able to go to the gym tonight tomorrow. I have a really busy day I'm like I wake up at five and we got workouts and then I have class all the way until five o'clock, so I Got a 12 hour a day tomorrow. So that's gonna be interesting To see how this goes. I still have a lot of work to do tonight and edit this video And I gotta go print some stuff out in the morning before I go to class First thing I'd like to say is I apologize because the last thing I want to do is bring You know, I want to keep a positive vibe and everything. I don't like you guys see me in this state of mind I don't think it's right, but I'm not gonna miss a upload I'm gonna make as many videos as I can for you guys and I'm not gonna miss a upload as he has no upload, you know Tuesday Thursday Sunday, and I won't miss one I'm gonna make sure I upload a video every single time Even if I'm not in the right state of mind like this, that's no excuse So hopping into what I want to talk about today because I've got this question multiple times Whether it's between personal friends or whether it's between fans or just comments that I get online and It is is YouTube worth it. You know that statement right there. I mean, that's just a simple question Is YouTube worth it? What what does that mean? You know, it can be many of things, you know as YouTube or if I guess the time In result of the money that you make or is YouTube worth it as in You know posting the content on the platform, you know, you can go many different aspects through this But I'm gonna explain my thoughts on it on what I think saying that statement is a broad statement So is YouTube worth it? in my opinion, I Don't do YouTube for the money If I did YouTube for the money, then I would be out of YouTube Years ago because it is not the best money unless you're getting a ton of views I mean a ton of views.  But that that's not the reason why I started I started YouTube when People really weren't focusing towards YouTube as a money source I honestly didn't even know you could make you to earn money off of YouTube when I started my YouTube I mean, I was younger. I didn't know I just wanted to make cool videos. Like that was my like my passion was fishing I wanted to spread the love with other people on the show my fishing trips. I wanted to you know Teach people more about fishing. That's what I wanted to do. You know, it wasn't ever about the money So saying is YouTube worth it. It's a hundred percent worth it if you're going to you know, push it towards something that you love I think that's very important. And that's that's the the true meaning for it You shouldn't be pursuing YouTube for the month. You shouldn't like if you're pursuing YouTube for the money Then honestly, I you should quit right now I'm just being serious with you because if I was pursuing YouTube for the money Then I would have quit like I said a year or a year or two ago when my channel like taint Because my channel is at the bottom lower right now So bottom lows has ever been and I've just been cruising. I haven't been gaining. I haven't been losing I've just been cruising and I'm just making this content to support You know, all these all these people are supporting me on the videos like you guys like my supporters Like I can't just go drop off the piece of the earth You know, I know I inspire a lot of people and therefore, you know, I see it every day I'm a fan today or two fans today It's just it's just really unreal guys and that's what I enjoy about it. It's not about over the money You're gonna make an incredible YouTube right now. I make a good amount of money on other things, but not YouTube YouTube is my lowest income source. I promise you anything else. I'm doing you gotta enjoy doing that That's the biggest thing if you're gonna start YouTube You need to start it because you enjoy doing it and you want to make videos or make content to inspire others You want to make videos you want to make content to put out value or you want to make videos and make content over something that you have a passion for This is as simple as that. It should never be, you know, is it worth it because of money? It shouldn't ever be that way. I'm just stating that because of the questions so broad You know, I could go either way with it You know, is YouTube worth it because of money or is YouTube worth it because all the time you have to put In the videos because I'm gonna tell you one thing if you want to get anywhere on YouTube You gotta be consistent because it's It's just like a TV show, you know Say there's two new episodes a week on a TV show and they miss two or three weeks like It's just gonna slowly dive off of everyone's mind like you gotta consistently do it no matter what it is in life It's like going to the gym What are you gonna go to the gym three weeks in a row and then skip three weeks and then go three weeks again? Like it doesn't work that way like you got to be consistent That's gonna be a sacrifice that you have to be willing to take it's putting in the time putting in the work Know that eventually something's gonna come out of it and know that you're enjoying what you're doing That's the biggest thing and that's what matters I wanted to talk about this topic because I've actually got asked this question multiple times I've had a lot of buddies wanting to do YouTube and I've had a lot of people come up to me Wanted to do YouTube videos because YouTube right now is pretty much the prime source like YouTube Everyone's been wanting to be a YouTuber. Everyone wants to be a vlogger Everyone wants to be fishing you like it is the crazy everyone's talking about it And so I thought it would be a cool video to talk about it All my opinion is YouTube worth it and a hundred percent yes If you're doing something that you love or you're doing it for a good reason if you're chasing it for the money Don't even hop into it. I'm being honest with you don't even hop into it You want to do it because you enjoy doing it and that's what matters no matter what it is in life guys I'm sick guys, but thank you guys so much for watching. Thank you guys so much for the support If you could please smash that like button comment below and subscribe and hit the little bell Hope you guys are grinding every single day working hard Striving to be the best you could be I think it's so important guys to work hard every single day towards your goal Thank you guys so much for the support. Let me know if you guys want some daily vlogs some more vlog style Like this wasn't much of a vlog But I want to start equipping more vlog style. So let me know below what you guys want to see next Thank you guys so much for the support.  Don't be normal. We're gonna change the world guys. Thank you guys so much for the support I'll catch you guys in the next


Thank you to all of you, to Gülsino Hans especially for the invitation, and for all of you, and to allow me to share with you some thoughts about Switzerland as usually when I'm talking about that tiny, not so important country over there in the Alps, you know. Sometimes people are interested in that country because one says it's a sort of example of good democracy. And maybe this is not that true. The title of my presentation is this, Swiss Confederation 2023. This year is an anniversary year, and what about the last 25 years ahead? Again, this is what they celebrate. This year in Switzerland, this beautiful picture, isn't it nice? I mean, these allegorical figures, you know, that's the new constitution. In the middle, you see that lady on the throne, so to speak, that is Helvetia. And beside her, this is something like Mr. Switzerland or so with the flag. And then you have the economy on the one side, the civil part of the population on the right side. You have the military part. You see that nice angel or something like that in the heaven. This is the one who pronounces peace. They have made a peace. They had some differences. In the meantime, they have peace. They have found together and adopted their new constitution. The paper this lady has in the hand is the new constitution. And if you look at it closer, the date that is written there, that's September 12th, 1848. So this means that now we celebrate, let's say, they celebrate in Switzerland the 175th anniversary of the birth of modern liberal democratic Switzerland. This is what the mainstream says. This is what is in the history school books, you know. We heard about this is the official celebration this year. A couple of days ago, on the 12th of 2023, there was the official celebration in the parliament building, things like that. So that's what I'm now talking about. How did it come to this beautiful event of that new constitution? In 1815, they entered these 22 cantones, entered in a looser confederation. So that was not a tight state constitution or something like that. It was a confederation, a relatively loose confederation. I put everything in blue, what has to do with freedom, with libertarianism, with anarchy, things like that. And I put in red what is the opposite of it. And while they had this loose confederation, I think that was a quite decentralized, useful treaty. Within this group, the so-called liberals developed a quite extreme aggressiveness against the conservatives. They even attacked, sort of militarily, some small warlords out of the liberal cantones, went, for instance, to Lucerne, which was a conservative Catholic canton, in order to remove their government. That was not successful, things like that. But these attacked cantones, the conservative Catholic cantones attacked. They made what one does in such a situation, they made a treaty among them in order to defend themselves against their aggressive colleagues in this confederation. That is the famous Sonderbund, this special treaty, this defense treaty. And Sonderbund, something like a separate, separate treaty, means Sonderbund. And of course the liberals are outraged, that's against our rule we have, you are not allowed to form your own Sonderbund. They started the Sonderbund war and they won the war, the liberals against the conservatives. So these aggressive liberals started the war and won the war. And of course they used that as a pretext, not only to dissolve the Sonderbund, which would have been the logical consequence, but to implement a new constitution, to enforce a new constitution. And now you see the figures how this constitution became into force. There were 15 and a half cantones that adopted this constitution. Of course that were the winning part of the Sonderbund Creek. So the winner out of their strength position they implemented this constitution. This half, 15 and a half, this is because some cantones had been divided earlier. That's why not just 15 cantones, but 15 and a half. And for this constitution, while the loser of course, approximately there were some neutral cantones as well, but in principle the loser of this war were against 6.5. Now unanimity would have been necessary in order to form a new state out of a group of principally independent small states. It's not possible to form them together just by majority. And this was generally accepted by international law, by state law so to speak, what that kind of state was concerned, it was quite clear unanimity is necessary in order to form a new state. But they were the winners and that's why they enforced it. In other words, this beautiful event here, you should write it not in blue letters, but in red letters according to my, you know, color principle. That was not, I would say, the birth of modern liberal democratic Switzerland, but it was illegal coup d'etat. That's what we are celebrating this year, strangely, but I think these are the facts. Of course, they call it differently now, the mainstream from the left to the right. Everybody says, no, no, no, that was not illegal, that was revolutionary. They put it in blue, you know, and say that was liberation, a revolutionary revelation from the ancien régime that was against the conservative cantones, you know, and that's why this looks a bit like King of France or so, and they resisted against that and that's why it's not quite illegal, it's revolutionary. And they have an argument, so these official historians, they say around Switzerland and other countries, too, there were revolutionary movements really against ancien régime authorities, mainly not quite successful at that time, maybe later when these national states were created, and that was just, you know, such a revolution in Switzerland, but that's not true. In Switzerland, they did not stand up against, you know, some higher ancien régime structures. What we have here is something different. Again, in red, I would say an aggressive subjection of defensive, peaceful, conservative cantones. So that was not revolutionary, that was just simple, illegal. So I would say that constitution is an illegal constitution, and this is what they celebrate this year. Now, one could think, okay, that was a stigma of that situation, maybe in the meantime, this was healed, the stain was wiped out, but this, too, is not the case. There has been several partial amendments of the constitution, but there have been two total revisions. They call it total revision, and here again, first we have again this new constitution of 1848 with this continental majority, I already mentioned, 15.5 against 6.5. And by the way, it's not only a confederation of the cantones, but also of the people. They did not only count the cantones, but also the people. And if you look at it closer, of course, there were more yes than no, but there were very few only people that were allowed to vote. And that's why if you compare it with the whole Swiss population at that time of 2.4 million people, those who approved it, explicitly approved it, wrote yes on the slip, these were 6% of the population. Of course, one can say those who did take part, these were a sort of representation of the whole population, but I think 6% is a little bit small to be able to represent the country. So these were the figures 1848, and now what these two further total revisions are concerned, unfortunately, that was not different. We see that here there was a revision in 1874. The very same cantones, almost the very same cantones were for this revision, and again the same parties, you know, winner of Sonderbund and loser of Sonderbund, there were even two more cantones against that. So it was even far away from this unanimity that would have been necessary.  Again, that's really, it seems, a stable relationship. 13 cantones pro and ten no. If you count precisely, there is one canton more in the meantime. Canton Yura came to university, one canton was divided into two, and that's why the sum is one more. And what the population is concerned, you see this is a bit higher than in 1848, but it's 12% in 74 and 13% about the same ratio in 1999. And one can ask, is this representative, where do they take their right to, you know, give a constitution to the other 87%? I do not know, but so this means that this stain, this mistake, this illegality in the original constitution is still there. So that's what I wanted to share with you about the celebration in Switzerland, but now it's only a quarter of an hour, and that's why I add something else. So how shall we deal with this? I mean, is this the situation? Okay. Or shall we try to put it in a broader context? And in order to do that, I would like to go back to this gentleman. Maybe you recall him from my speech two years ago in 2021. This is the famous, at least in Switzerland, the famous William Tell. Blue, I take him in blue of course, because he is the anarchist. William Tell is a mythological person, of course, in 12,191 he killed the tyrant, and it's typical for him. He doesn't speak very much, he acts. He doesn't go to assemblies in order to discuss political issues, he acts. That's why this famous sentence of him, everybody in Switzerland knows it, the axe at home often saves the carpenter. So he builds his house and repairs his house with the axe. He doesn't need anybody else. He shoots the tyrant not with the axe, for that he has the crossbow. That's William Tell, the anarchist. And on the other side we have this gentleman. He is called Hermann Gessler also out of this drama by Frieder Schiller. And he says, I'm the empress servant. He is the embodiment of the top-down approach. He is the representative of power, or one can say he is the anarchist. You see, the anarchy is not as, as you know, something like un-order or so. Anarchy means without archer, without predominance, without monopolized power. This is what anarchy means. And the opposite, I mean, without this negative part is archism. And that, in my understanding, is an archist structure. And Hermann Gessler is the, you know, personification of archism. And then, now we are trying to put that in a broader context. What I developed then two years ago was this, that I said here on the arrow of the history and the starting over there in that mythological story of 1291 with, on the bottom side I put the archist part in blue, on the top side comes the anarchist in blue and on the top side the archist in red. That's why Gessler is there and Tell is on the bottom side. Now we have this tradition I showed last time. This anarchist tradition, one could say, of Switzerland. They never had a center in the sense of a capital or a common government or something like that. That was always a treaty, something loose, with a lot of conflict, spirit between Catholics and Protestants or conservatives and liberals, as I showed you before. That was typical. That was not paradise at all, but that was anarchism. In a way, until this happened, when Napoleon came a couple of centuries later and introduced this Hilfetic Republic that was a unified, Napoleon-minded, liberal country, but not for a long time after Napoleon, they had this treaty I mentioned before, this confederation. And then, as we know, in the meantime, we had the Civil War, we had the illegal Constitution of 1848 and then we have this, one could say, the archist development. One could say, until mid of 19th century, they have more or less this anarchist tradition and then it changed to the archist development. By this event, they celebrate this year. Of course, and during that time, ongoing concentration of power. So we have this broader context, what the Swiss history a bit more back is concerned. And now, if you're still alive and awake, yes, it's fine. I would even broaden more of the context. Also, recalling what I showed you two years ago, the even bigger picture. Maybe you recall this. Again, we have on the bottom side this anarchist cultural, behavioral development, going back to the Neolithic Revolution, agriculture, sedentaryness, and a big part, at least, of humanity that was still in decentralized, not monopolized structures. For instance, Switzerland, you see here, with the timetable then, what we saw before, but that was the prolongation of a much longer anarchist tradition of humanity. But, as then I showed you two years ago, some when in the past, not as close as this Swiss history, but some thousands of years earlier, around 3000 before Christ, this new phenomenon of states all together came up. Namely with these big city-states in Mesopotamia as a new phenomenon. And then one could say that from that time on, there was still developing and concentrating history of power with the Roman Empire, with absolutist states, with the national states, then we come to our closer story. So this is the even bigger context with the state all together to put our Swiss story into that story. And of course, like always in these red parts where these anarchist structures are at work, it's accompanied by battles, by wars, such as, for instance, world wars. This is typical for the red part. That was the broader context.  We have that other context now in mind and are going to this. As I told you, on the 12th of September, they celebrated Happy Birthday. Actually, now to put it more precisely, what do we celebrate? In the meantime, we know it a little bit, but just to summarize, what we celebrate is that civil war, the illegal constitution. What we further celebrate is, for a long time, the Catholics, those conservative cantons, were excluded almost out of the political discussions in the parliament, in the government, on federal level, they did not get a noticeable representation. In war times, of course, Switzerland, like all countries, made their martial law with mandatory draft, mandatory constriction, that's not untypical for states, things like that. Then, for instance, these are just examples. The permanent war tax. This is a nice story in Switzerland. During the Second World War, they introduced by martial law a tax. Versteuer. Ver means defend. It almost sounds like war tax. Versteuer. They introduced it not in an official statute, in a legislated statute, but in an ordinance from the government. Beschluss, außerordentlich Beschluss, exceptional decisions, something like that. After the war, they did not stop with that. They said, we need a little bit more. We have provisionally to extend this decision for some years. After some years, they said, I think in the meantime we really do need it, and they extended it even more. Sometime, that was not a decision, an ordinance anymore by the government, but an official statute with the same content, but still called war tax. Then came the moment where they said, now we call it direct federal tax. Since then, the federal taxation plays a considerable role. This is what we celebrate, too. Then, all these typical wars states make, such as war on drugs, total prohibition of many drugs, war on climate change, which is very like in other countries, maybe with little nuances, but in principle the same as in other countries in Switzerland as well, and very prominent, the war on pandemics, also perhaps a little bit less intrusive than in other countries, but not really with difference, so this war on pandemic. I think that was a very crucial thing in this history. I'll come to that right afterwards. And so it goes on, all these fashionable wars. Besides that, the ongoing centralization of power, the cantonese loose power and the center attracts power. That's a natural law, so to speak. So this is what we celebrate. It's not to celebrate, it's to deplore, I think, or it's to complain about, but that's what they celebrate about. It seems that this is a pattern. Of course, this is not only in Switzerland, of course not in other countries. To compare it with a very prominent country, we have approximately the same picture. I cannot say much about that. That's not the point now today, but a lot of you know much more about this. But in America, with a sort of comparable constitution to the Swiss one, we also have such things. By the way, there is an interesting difference. They had the constitution. If we take the constitution of 1787, that was adopted by all colonies. That's a crucial difference to Switzerland. So that was not a majority, but those 13 colonies, they had to adopt in a certain process, over a certain period of time, and then they get into force. That was their basis. But then the Civil War didn't come before, it came after. The Civil War took place, of course, and that was quite comparable with the Unionists that correspond a little bit to these liberal cantones and the Confederates that correspond to the Sonderbund. With a lot of differences, of course, but there is some interesting parallel between these. And then a lot of wars, which is typical for states and also the United States. I do not precisely know when they celebrate what. Once they had this bicentennial, but that was not from this constitution, but that was from the Declaration of Independence. However, maybe they also think one should celebrate something. Now, we have still more time, a quarter of an hour. Is it still okay with dropping in, maybe, or so? Now the future. I have to say something about the remaining, about the next 25 years. This is what I thought about, 175. What about the bicentennial? The Swiss bicentennial, what's about that? Now, again, to keep that in mind, we have come to 2023. We have this war on climate change, the war on pandemics, the war on generity, the war on whatever. There are always reasons for the states to make war. And now I think maybe this is a consequence of this COVID nightmare, that certain tendencies come up that were not articulated in earlier times, but now because people realize the danger of such a structure, such a monopolized structure, they begin to think about it. And that's why some blue elements maybe are coming up more strong than in earlier times. There are grassroots organizations. I always now speak about Switzerland, maybe in other countries there are similar things. And these are sometimes a little bit crazy organizations, but it's the sign that people think, what is this all about? We do not need the state, we can do it ourselves. And grassroots, they use this word, grassroots is quite good. All these grass pieces and they belong together somewhere on the ground. And these are interesting movements. And they are very critical through the state. Other new movements maybe, especially again, that had resisted, that had organized demonstrations against this COVID hysteria. And they are still existing, these movements, and they participate in the election. Now there is an election term of the national level, and some of them do do candidate, do present candidates for this. Of course, they have the risk that once they are elected, they become part of the system. That's often the case, but maybe some manage to, you know, change things. But in any way, it's a sign that it's not that clear and accepted anymore that there is a state.  They discuss, I think among you also some, about alternatives to the fiat money. Or this is a sign, perhaps, that doubts about the faith in the states are coming up. And I think the faith in the state is probably the most important basis of this structure. I mean, it's ultimately perhaps a very unstable structure. I can imagine the state because it's fully artificial. You have to have huge organizations and intruding procedures and surveillance and all these things just to maintain the system. And maybe all this won't be sufficient unless the people believe in this structure. So the faith, I think, is a very important thing. And things like that, maybe these are not yet very important things, but they could be signs that this faith is fading, you know, with tax avoidance. I do not mean just tax evasion and tax fraud. That, of course, takes place always more or less today, more or less than more. But the attitude of people that say we behave in other ways, we go back more to, you know, exchange economy. We do not pay in the official money way, but in other ways among our group, things like that. And they sort of evade state-based influence. There are tendencies in that direction. And now one can speculate when, in some years, 2030 perhaps, so this goes on, this phase, maybe they say the state. Is that just a firm? Is that a player, an actor? Today already there are some movements that articulate that very much. The state is just a firm, that's just a player. He also is filed in some business indexes as an actor. This means this is not the state anymore, things like that. So all this and thinking about statelessness could come up. Maybe due or thanks to corona. And once this is going on, let's say I thought, now I'm starting to dream, you know, but why not? I thought that, can you read it? Tax resistance, then exit declarations, that happens already today. That people say I do not want to be a member of that club there. And here is my declaration, I withdraw my membership without being forced to leave the country, of course. Of course these letters will not be answered, but people think about things like that. Or then I thought, I dreamed that once these declarations are there, once a certain broader tax resistance, that rating agencies think about the rates of these government bonds. Are they really still AAA or are they already junk bonds? Why not? Some ratings have already been reduced. And the more such discussions come up, the more this could take place, even more with more weight. And then they start about thinking why not winding up some parts, at least the most negative parts are necessary part of a state. Why not liquidate this part? Why not privatize? Now this is really within this dream, but why not to think about that? Why not to see signs for a certain development that could go in such a direction? It's not more than a dream, but nevertheless it's that. So that there is a general decline of this power, that it's not just continuing, that it goes even in a fall movement. And why not on the 12th September of 2048, we get the final report about the Swiss Confederation being winded up. All debts paid back, not all of course. A small dividend perhaps only, but the file is closed. That was what I dreamed recently. And in this case, one could say these balance there to celebrate the birthday this year can be, you know, flow away. And we can, instead of that, this happy ending. Now just one more slide to broaden even more, or again to broaden our view to come back to this. We have now the whole state-based context. We have these 200 years. I just presented what tiny Switzerland is concerned. We have this rising phenomenon from the blue to the red part that goes back again after 200 years. We have bigger players like the one I showed you before. For instance, the United States of America where a similar phenomenon could take place. That lasts longer of course. That's a torsion polite. This is what we talked about, this accounting principle. Last in, first out. So Switzerland, last in, first out. United States, earlier in, later out. And first in and last out will be the overall phenomenon of state structure. It will last even longer of course, but why not be within the same context, within the same tendency.  Switzerland's state is liquidated, other states as well and so on. And maybe, I'm still dreaming of course, maybe on the global level we have the same tendency. And then one could say, we resume so to speak these decentralized anarchist structures that were interrupted somewhere by this state-based time. And once this is made, then really we can say we have a beginning. Thank you.


Yeah, now it's now it's on. Okay. Very good. Yep. Okay. Great. So we are happy to have Stefan van der Rijn the next speaker Thank you. Welcome everybody I'm still a bit sleepy because I arrived in the middle of the night. So I'll try to be as sharp as possible and To make me even be awake further. Please do allow a lot of her or please do ask a lot of questions So that makes it more lively and I get more feedback Very good. I see my lectures a little bit as Serving to the other lectures in the sense of building up and introducing certain topics that will make certain following lectures more accessible and so I thought to Really give some basic introduction also to aspects of supergravity and also black holes Of course when we talk about black holes and supergravity, we first have to learn a little bit about supergravity So I thought I spent some time teaching you the basics of Supergravity with and without matter couplings and then also discuss some black hole solutions in it and so I tried to do this in a kind of like sort of Little bit of a from a new point of view or a different point of view as you might usually see also to to well To make it not too technical Probably everybody has seen once this book and you can just lecture 500 pages or thousand pages about supergravity. So I kind of like distilled what I needed from it and Well, let's see how it goes So let's start with something really simple before we go to n equals to supergravity I want to go to just minimal supergravity and in fact even let's forget about supersymmetry for the moment Let's think about the gauge principle where the simplest set up is that we have a gauge field and a gauge transformation which involves a gauge function epsilon which is a scalar function and Of course, we know how to make gauge invariant quantities by constructing field strengths The action is then just f mu nu squared and this is all of course well known so what you can think about now is is is to Change this principle of a u1 gauge symmetry where you promote this epsilon this gauge scalar function into a spinorial quantity I want to change this into a spinorial quantity by Trying to come up with a gauge principle that has a spinner Epsilon is a spinorial quantity and so if you do this, of course, you have to change something on the left hand side as well and so well the most kind of obvious thing to do is to add here make of this thing a spinner as well and We give it of course a different notation It's going to be the gravity no later on but for the for the present remark I don't even need to be in there has nothing to do with gravity at all. So This spin zero became spin one-half and this spin one became a spin three-half and of course because this is spinorial it has to be anti commuting and and This field here is a spin three-half field and you can make similarly a gauge invariant combination Now I suppress the spinner indices This here is clearly invariant under this spinorial gauge transformation and of course you cannot repeat the same trick in making an action say this is F mu nu squared This we cannot do F mu or if you call this for the moment that this this you can call this psi mu nu You cannot you cannot make an action with psi mu nu. We know that for spinors. We need first order actions and with first order actions They only need one derivative and so the action that We write down for it is the Rita Schwinger action. It was I think written down maybe even in the 30s or something You can do this in arbitrary dimensions and so the new Siro This is a Rita Schwinger and it is gauge invariant because for the notation If you want to look up the pluses and the minuses I followed this book here by Friedmann and von Poehen which I recommend for both students and staff and This is of course on the symmetric so that means that here only the field strength for this spin three-half particle is Is is there? So this is a spin three-half particle And so people have been playing with this action before the days of supergravity even Either in Schwinger And so if you count the number of degrees of freedom of shell degrees of freedom then Yes, because This is invariant under this transformation and here only the anti-symmetric part is Is present because this this gamma mu nu is essentially the product of three gammas totally anti-symmetric on the three indices Yes, but you can do partial integration here You get a d mu you partial integrate and then it's this and then it's the d mu d nu that that makes it invariant. Yes, very good Very good. Please do ask. Yeah Even if you know the answer very good host choke number one Very good, let's count the degrees of freedom a spinner has of course Dimensions two to the power d over two the even part or the integer part of it. That's the number of components But then this in this this this has a this on top of it It's a Lorentz vector, so it has d degrees of freedom extra So you would multiply this by d, but you have to subtract one because you have one spinorial One spinorial gauge degree of freedom that you can subtract so that the spinner Is again two to the d minus one So you have d minus one times two to the d over two off shell degrees of freedom and then d equals four We have 12 so an off shell Gravitino has 12 degrees of freedom This is my arena. That's also important Indeed in n equals although this is not yet supergravity, but in n equals one supergravity We're going to have one gravitino, which is my arena in an n equals two. We're going to have two my oranas or one dirac Fermion Okay, so now I can couple to gravity and we know of course that if you couple to gravity We're going to introduce wheelbinds And these wheelbinds from these wheelbinds you can construct a metric Can use this here and so the metric is constructed out of a wheelbind just to set a notation and you can try to Assign a transformation rule because we know that this is going to couple and so now I'm going to Enter supergravity And so the wheelbinder on the supersymmetry has the following form Well, you can ask how was this derived that that is a little bit more difficult to explain Essentially how it historically was derived was by trial and error and Here's the spinor Super supersymmetry transformation gamma matrices and the gravitino so the graviton transforms into the gravitino And so that means the delta g mu nu Is just epsilon bar gamma mu Sign u symmetrized And so we have a metric here and the off-shell degrees of freedom of a metric is We have a symmetric tensor. So that's one half d d times d plus one But this metric also has general coordinate transformations just like a general relativity. These are d So you can impose d gauge conditions so then You subtract d and that is then of course one half d times d minus one and in d equals four We have that is just six So if you want to build the supergravity theory Having equal number of bosons and fermions you see immediately at least if you want to do that off-shell You see there's a mismatch here. We have six bosons and we have 12 fermions. So that doesn't match But of course, this is an off-shell counting and if you just want to do on-shell supergravity It's sufficient We know that off-shell This six goes into the two polarizations of the graviton on-shell And this 12, this is an exercise that you can do this 12 on-shell Also goes into two That I won't do here in this class because it's a little bit playing around with the equation of motion for the Rarita-Schwinger field It's standard techniques that you also do for the Dirac field except you have more indices So you you do more than with Dirac just happening the degrees of freedom Um And so you can look up the argumentation in this book or ask me separately if you If you want to know how to count the degrees of freedom of a spin the on-shell degrees of freedom of a spin three half Then the answer is two try it first yourself if it doesn't work, please ask me So on-shell we do have a matching And of course the first supergravity theories were constructed by well Friedman Ferrara for newheisen and so I'm going to write down the answer and restrict myself now to four dimensions So n equals one supergravity is a minimal supergravity. It's not coupled to anything yet There is no matter But I'm just writing this down also for the purpose of setting the stage explaining the conventions This here is a covariant derivative is no longer a flat derivative And the covariant derivative also involves the spin connection and the spin connection is not a new Is not a new field it's determined in terms of the wheel binds By formula that probably I guess you all have once seen and so The variation of the Because this is no longer a flat derivative The variation on the supersymmetry of the gravity, you know is something like And here you have the spin connection epsilon So that is this d new effect And of course, uh, this is going to be important when we discuss also bps solutions because bps solutions Are solutions to the equations of motion that preserve some supersymmetry. That means it's annihilated by um, a particular epsilon Um, on the right hand side here Now this is n equals one supergravity It contains just the ordinary gr plus the spin three half field If you're interested in black hole solutions that have no fermions excited Then you look for solutions that have the fermions set to zero in this case There's only one the spin three half you back to gr The schwarzschild solution and the curve solutions are solutions, uh of this, uh equation of motion of this theory And uh, but they don't preserve any supersymmetry. This there is no epsilon for which, uh, uh, it leaves The solution invariant also even the the extreme curve Solution is not a bps solution of um, uh of this theory You can also, uh, add additional terms and construct again with the same number of fields can construct a Supergravity theory that doesn't live in In asymptotically flat space, uh, but it lives in anti the sitter Uh space so you can extend this So let's call it ads supergravity Or if you don't yeah, well ads supergravity Is it just a deformation later on? We will see this deformation is a gauging And ads supergravity is let's call this as as zero Then s equals s zero plus one over two kappa squared integral d four x Square root of g or the determinant of the wheel binds also sometimes used and then we have One over l is a deformation parameter. This looks like a mass term for the gravitino And then there is a cosmological constant And if you write down the equation of motion, then, uh, you will see that until the sitter space is a solution of this With a cosmological constant cosmological constant so r mu nu Equals uh minus three over l G mu nu so we say that lambda is equal to minus three over l Being negative Okay, of course when you deform the action with a parameter l here that that Well, this isn't very important for on the supersymmetry for any l, but you have to adapt the Transformation rules and for instance the the transformation for the View bind remains the same but we get for instance additional terms like this here d mu Minus one over two l gamma mu epsilon And that is the supersymmetry transformation rule that leaves this this action invariant, okay Good are there any questions about this? good, um, if not, so this is the story basically that Uh, is a story of the of the 70s When supergravity was first discovered and I did hear an off-shell counting and off-shell matching of the degrees of freedom But what happens if you want to construct off-shell methods? This is useful for both Well applications to do with localization. We're going to need an off-shell formulation Uh, in fact also in field theory in the localization program You often need the gravitational background as a as a background not not propagating, but you all you often need off-shell versions of of supergravity And so this will be important also for the black hole story and the lectures of Of some near murky in particular So, um, you see with the with the off-shell we have a problem because we have six Uh, we have six bosons and 12 fermions degrees of freedom. So there's a mismatch. So how to restore this Um, I want to explain this Uh, of course later in n equals two, but at this moment, uh, also in n equals one And this makes use of a program that is called the super conformal calculus Now this is something very technical many people would run away. So maybe we'll lock the doors um, and um I'm not going to give all the full details. I want to give well the ingredients of the mechanism and um Emphasize the most important points So the off-shell methods We're going to use super conformal methods or calculus also called So of course conformal symmetry is something very important in our, um field of research also for field theories So some of these aspects you have even might have even seen or learned about just in the study of super conformal field theories without gravity And so what is the idea here? So well first of all before let me repeat that the problem was that we had That we had six bosons and 12 fermions. So there's a mismatch. We need to introduce auxiliary fields and so, um Um Historically people tried by trial and error to add these auxiliary fields and so we need to add essentially Six auxiliary fields six bosons And that can be something like a gauge field a massive gauge field It would have four degrees of freedom and then a complex auxiliary scalar field I will I will I will make that more explicit in a moment Uh, or you can add a a gauge field with a gauge symmetry and An tensor field And if you do the counting then you get an off shell matching, but let's see how that comes out So I want to explain here what the super conformal method is the idea is to construct super gravity theories That first have a much larger symmetry namely super conformal symmetry The hope is that when you have more symmetry symmetry is more restrictive. It's more constraining So it should be easier to write down actions for it and and How then to construct ordinary? Super gravity well, that is by gauge fixing procedure gauge fixing all the generators That are in this algebra for instance the dilatation and later on the r symmetries that are going to be Um Part of this algebra, but not of the Poincare, but we'll we'll we'll do that in detail Um, good. So let's first get the main idea here forget about supersymmetry. Just focus on gravity by itself So we can consider consider the action The action based on the Lagrangian L is square root of g or minus g And then we have one half d mu phi d mu phi Plus one 12th r Phi squared and if you look up the conventions about the metric here, this has the wrong The wrong sign kinetic term, but uh, that's not important for the present purpose or not too much This action here is gravity coupled to a scalar Hitchy scalar times the scalar field here and it has a dilatation or a scale symmetry And the symmetry is delta of Phi equals lambda is the parameter from the dilatations times phi and delta g mu nu Is minus two lambda d G mu nu you could check explicitly that this action is invariant under this scale symmetry And so whenever we have a gauge symmetry, we're allowed to do gauge fixing And it's kind of clear how we should gauge fix to get general relativity out We should fix phi to a constant then this term disappears And if phi is a constant then this becomes Newton constant Of course, we know this also from string theory where we uh, often This is called the dilaton field then or the exponent of it So we gauge fix since we have a local symmetry this this parameter is allowed to be dependent on x as we can gauge fix And then phi is equal to square root of six over kappa Newton's coupling constant And so, uh, then of course we get that l equals one over two kappa squared times square root Of g r Alternatively, you can do something else You can start with gravity Einstein general relativity and introduce a scalar By saying, um, well, we're going to take grab or alternatively we can take gravity and introduce um Or introduce g mu nu prime by definition kappa squared over six g mu nu times phi squared This combination here Is invariant under dilatations because here the weight this has weight minus two This has weight one So if we put phi square here, this is invariant under dilatation And if you define this combination you rewrite the action You'll figure out that you can rewrite the action in terms of g mu nu prime And then you just get Einstein-Hilbert term on the nose That's not a surprise because this is how it was constructed. You can start from Einstein-Hilbert action Write this metric in in this form By introducing a scalar field and rewriting it such that you introduce now dilatation symmetry given by this If you plug it in in the Einstein-Hilbert action, you get back this You can see it reversely by introducing a scalar field that compensates for the scale transformation that Einstein-Hilbert does not have That's why this phi field is called a compensator Yeah, so this is a simple trick to to make Invari actions invariant under under scale transformations If you had a theory that was not invariant on the scale transformation You could make it invariant on the scale transformations at least at the classical level by introducing compensators that account for The right scaling weight in a scale invariant theory I'm not doing anything quantum here. I'm also not talking about conformal gravity in the form of Well, you can call this conformal gravity, but usually People call conformal gravity based on the wild tensor. The wild tensor square is a higher derivative theory That is also part of the story once you include higher derivatives into this game You will get the wild tensor square. I don't know if you will talk about higher derivative terms Maybe touch it. Yeah So I will not do this. I will not include any higher derivatives in my lectures here Good. This is the main idea of the super conformal method. Just add some fields to compensate for The lack of scale invariant or start with theories that are conformally invariant and gauge fix all the all the transformations that Or the symmetries that are not part of coordinate transformations We gauge fix them such as you end up with just coordinate invariant theory Now we have to just repeat this game in supersymmetry The idea is still as simple But the technicalities become a little bit more involved Because everything has to be well sitting in multiplets in off-shell multiplets So this compensator needs to be part of a multiplet itself And in n equals excuse me In n equals 1 supergravity that is still quite simple But in n equals 2 supergravity that is a little bit more Involved So let me say a few methods about or a few let me make a few remarks about super conformal symmetry Because that's also useful perhaps for Your general knowledge So there's a super conformal algebra and the generators Of super conformal algebra Kind of can be depicted as this It's a super algebra. So it contains bosonic and fermionic generators Here it contains here Here there is the conformal algebra Which in four dimensions is just SU 2 2 which is SO 4 2 Up to double coverings but these double coverings are important when you discuss fermions and we are discussing fermions And here are also bosonic generators and there are symmetries There can be one or there can be many And here are the supersymmetries we call q But the supersymmetry that's not the only fermionic generator The supersymmetry the supersymmetries are kind of the super partners of the general coordinate transformations But the conformal algebra also has all their generators even apart from the dilatations also has special conformal transformations These special conformal transformations have their own super partners. They are called s supersymmetries And these generators here are on the off diagonal because they transform if this acts on bosons fermions Then a q and s transform bosons into fermions. Whereas these They transform bosons into bosons So in n equals 1 d equals 4 This super algebra well has the notation su 2 comma 2 slash 2 And it contains as a bosonic super algebra contains the conformal algebra Which is isomorphic to s of 4 2 Times u 1 And that is the r symmetry called the r symmetry 1 yes i'm already in a In this n equals 2 setting very good in my notes. It's fine So the conformal algebra Contains of course the translations. There's four the Lorentz transformations that six Then there are special conformal transformations. That's another four and then there's dilatations that one So these are the generators are pa for translations the Lorentz transformations m a b the dilatations Well called a d and then we have special conformal transformations k a And of course only the 4 plus 6 is part of a Poincare theory So we have to gauge fix away both the um special conformal transformations and the dilatations And also the r symmetry r symmetry is not is a symmetry of the algebra But it's not a symmetry of a Lagrangian or at least not necessarily a symmetry of the Lagrangian But in a super conformal theory these are symmetries of the Lagrangian That's why we can gauge fix them if we gauge fix the super conformal theory We obtain Poincare symmetry where of course these symmetries are gauge fixed. So they're no longer symmetries because they're gauge fixed So r symmetry is not is not not necessarily a symmetry of a Poincare super gravity theory So now you have to make this is the algebra Maybe you can write down a few commutators to make that a little bit more visible For instance the ones you're least familiar with I guess is the ones that involve the s super symmetry So if you take for instance, well a special conformal transformation with a super symmetry I'm not writing spinorial indices here. Then this is gamma a gamma matrices times s For instance, if we do translations commutator with special super symmetry Then that's gamma aq Um, what else did I write down? Oh, we can have the s alpha s beta Now there are spinorial indices That's minus one-half gamma a alpha beta They anticommute into the special conformal. So that's very different from the qq anticommutator Anticommute into the translations these Objects here anticommute into the special conformal transformations And then perhaps one more q with s Anticommutes into the dilatations. That's a generator. That's a symmetry that sits in here Minus one-quarter gamma ab alpha beta times the Lorentz generators And then plus i over 2 gamma 5 alpha beta times t and this t is just the u1r The generator of u1r. So you see how everything mixes and forms one big algebra called the super conformal algebra So what we want to do now is to construct a multiplet That on which this super conformal algebra acts In other words, we want to find a realization of this algebra in terms of fields The next step after we construct the multiplet is to construct actions with it. But first the multiplet So we have a lot of gauge Symmetry is here And we know from poincare or from the gauge principle that once you want to make a symmetry local You have to introduce gauge fields And so, uh, let me make a list Let me make a list these these gauge fields they form a multiplet called a while multiplet and um So the gauge fields form the while multiplet Um, and let me make a table So we have the translations pa mab Dilatations special conformal transformation r symmetry And Then we make q and s Let me not make these sorry. I like to get the cosmetics, right? These are the bosons here and these are the fermions So, uh, what are the gauge fields here? Well for translations, we introduce a metric or or the field bind emu a For the Lorentz transformations while we introduce the spin connection But you know that the spin connection. It's actually not a independent field. You know the spin connection Uh, if you you can impose a constraint. It's called the tate hat postulate That's already in the absence of supersymmetry spin connection Unless you introduce torsion, uh, the spin connection is not an independent field. It has no dynamical, uh, physical degrees of freedom by itself They're completely determined in terms of emu a but we'll give them these names The dilatation It's one, uh, symmetry So the gauge field is just one vector field just like a u one And then here we have special conformal transformation. We call the gauge field f mu a and um, we call this here a mu And this here is of course going to be the gravitino And then there's a gauge field for S supersymmetry, which is also spinorial field psi mu So the degrees of freedom off shell Can be counted as follows now, um When we do an off shell count and we don't only count the number of components of fields We impose the gauge symmetry as well So we can use the gauge symmetry to subtract or to gauge fix certain components away We do not use the equations of motion. That means on shell So I already told you that, um, uh, uh, gravitone has six degrees of freedom But if I want to I can use the dilatations already to impose a I can I can make various gauge choices and later on I'm going to do another gauge choice But I can use the gauge the gauge transformation to reduce the six degrees of freedom to five And here I'll write down what I have gauge fix general coordinate transformations Plus dilatations then we go from six to five This year was not an independent field It's not an independent field. So it has no degrees of freedom Be yes Yes, but in supergravity indeed, there is a torsion Maybe I didn't say that the very precise enough, but the torsion is induced by fermion bilinears It's still the is still not an independent field the torsion component and equals one supergravity Is bilinear in the gravitinos and so You can still call that torsion But but my main statement is that there is still it's still in Uh, uh dependent field the the the the spin connection here Yes, yes, yes Yes, it can be written there's a formula that Expresses this in terms of the spin connection and in terms of fermi gravitino bilinears I could give you the formula in the break. Yeah Yeah, that is torsion. Yes. Yes, you could also the reason why I brought up torsion is that Uh already in general relativity you can introduce torsion in the game And of course the counting works differently in the bosonic part of it And here there's torsion, but it sits in the gravitino bilinear Yeah, uh for this one here Um Well, this is 16 So it's symmetric. So it's 10 In let's do it in four dimensions. We have 10 10 minus four coordinate transformation. That's that's six and that dilatation that brings it to five b mu here has d or four component fields But special conformal transformations are also a gate symmetry. I can use them actually to gauge away This b mu. So I'm very often one one picks a gauge where this b mu is zero So then there is no off-shell degrees of freedom here because I fixed here The special conformal transformations now A little bit of a longer story here, uh to see that f mu a is also not an independent gauge field There's lots of gauge fields here that are Not independent well the spin connection you all know but these this one and this one turn out also to be dependent on the other fields How can you notice well, you cannot really notice in advance what people do is you can you you construct actions and then you see that The equation of motion for f mu is algebraic It's like an auxiliary field almost It's algebraic and when you eliminate the equation of motion Then you find that f mu is a function of the other fields You can do in fact the same with the spin connection if you would not impose a tetrad formulaism and Postulate this one you essentially figure out that you can Use the equation of motion start with two independent fields and then use the equation of motion the equation of motion Will put omega as a function of e so that happens for this one And this one as well if you want to understand a little bit more in detail Then uh, you should really consult this book. Otherwise, I will spend too much time on this. Yes Yes Correct. Yes. So these different constraints I had exactly the same question when I was preparing this lecture and luckily better. David was still in utrecht So I could ask him like why should I choose this constraint? I don't want to choose anything What what happens if I choose something different? And he says, okay It's still the same principle. There will be the equation of motion, but it will be late Your our two choices will be related by field field redefinitions Well, you have to make sure that your algebra is of course holds of shell And then these constraints are usual curvature constraints And At least the way I understand the topic is that there's there's no Different choices that lead to different theories the different choices that you will make lead to Physically equivalent theories and the relation are just field redefinitions. They can look Complicated depending on what precisely we choose, but if you have a concrete example, maybe we can discuss afterwards Yes, very good How shall I phrase this? I can be of shell, but we still don't count this as dynamical degrees of freedom if you are an n equals 1 Well, let me Yeah That's right. Yes. Yes. Yeah, but that's still an equation of motion That's right. Yeah, that's the language in which we usually we impose a constraint Which can later on also be understood as an equation of motion But I agree that's a little bit confusing So I would like to think a little bit about this to answer this more more sharply. Yes Here we have a gauge field and that's three and Here this here Would have 12 degrees of freedom of shell, but we have more supersymmetry. I have engaged fix the s supersymmetry. That's the spinor So you can reduce four components out of the gravitino Further down to from 12 to 8. So here I fixed Both q and and s okay Yeah, I think the answers now Let me not tempt because I might give a wrong answer that these equations of motion are so special that even if you impose them You are still off shell if you you don't need the equation of motion in the To close the super algebra for these fields. I think that is the answer and so You're kind of both imposing question of motion But you're still off shell from the point of view of the closure of the super algebra But I will double check that to you Good. So now you see we have a matching because we have 8 here and 8 here Now this is not the end of the story here because With this this is a multiplet. It's called the wild multiplet But with this multiplet by itself you cannot make an action It's not because you have a multiplet that you can write down an action We've seen this already in this toy model for gravity Because we needed to in order to make the theory invariant We needed this compensator this compensator was a scalar field. There's no scalar field in here So to make or you can also say phrase that in different ways And this is maybe a chiral multiplet and in order to make a full density you need to Multiply it with another Anti chiral to have a full density I'm not going to go into too much detail At this moment. I think from the toy model Gravity you see that that we need a compensator the compensator is not part of the wild multiplet And so it is a multiplet by itself And that multiplet because it has a scalar field the most canonical thing of course to do is to Introduce a chiral multiplet compensator There's there's different choices for the compensator one is a chiral multiplet if you go to the gauge fixing You get old minimal supergravity if you use a tensor multiplet and you get to new minimal supergravity And let me for the moment just do the chiral multiplet So a chiral multiplet contains a complex scalar A spinner two components spinner wild spinner And an auxiliary field complex field f And so now i'm going to make this exercise again Now including Including this compensator and now the counting was somewhat differently Yes, uh for the dilatations. Yeah Well, it will do the entire job So, um So let's add this compensator here and do this exercise again We've seen in the in this toy model that in fact, I use the dilatation symmetry to to fix this scalar into a constant Yes, but I had already here fixed it fixed the wheelbine. I cannot fix fix the symmetry twice So i'm going to drop it here and turn this back into a six Yeah, then um, so i'm going to now add this list here to this list. I'm going to add Phi lambda alpha and f So how does it change then for me? It's easy. I just use the eraser here. You could just copy it or I will probably put my notes online as well or you can watch the video So here we make it a six and we only fix the general coordinate transformations um and so Oh, I'm sorry. I should put this here Phi lambda alpha and f So this is a complex scalar field if I have dilatations then if I have dilatations then um I can fix the real part of it or I can write this as a real part times a face And this complex scalar field is charged So it has a it has a weight under this one here And so i'm not going to eliminate a degree of freedom here I'm going to use the u1 symmetry from here and the dilatation from here to gauge fix this scalar If I do that I cannot go from four to three here So this remains a four And this becomes a zero What I have gauge fix here is that dilatations plus u1 similarly this eight here Was arising because I was using gauge fixing both q and s symmetry And so if you just use q supersymmetry, then I had 12 off-shell degrees of freedom And I'm going to use the s symmetry supersymmetry not to gauge fix the gravitino That would not be so smart because I want to have the gravitino as it is in point here I'm going to gauge fix this one away So then that this becomes a zero as well and I've used s supersymmetry to gauge fix the fermion in the chiral multiplet Then i'm done because this one stays there And that's two degrees of freedom And if all goes well, I should have now off-shell Equal bosons and fermions six plus four plus two is 12 and 12 from the gravitino So there's an off-shell counting of the While multiplet already including the compensator Well, if you go but that then then it's an on-shell. It's a little bit the same confusion as what I had here Of course if you write down actions for this this is an auxiliary field If you don't couple it to anything then this f is just zero But off-shell it is it has two components and this one you need for the closure of the super algebra Yes, well you have to go through all the details here And I that problem is going well It's not really a problem, but this this elimination of some of the auxiliary field is going to become a complicated exercise In fact also in the n equals two story Where I have lots of gauge fields that I can eliminate and they become functions of the other fields And then you have to figure out what that relation precisely is But for now I'm just giving you counting And so the action well, I'm going to write down the action You'll see what the equation of motion of f is it's still going to be zero And so the on-shell the on-shell action Sorry off-shell Supergravity This is called old minimal Is just s equals d 4 x square root of g 1 over 2 kappa squared r minus Psi bar mu gamma mu nu rho d nu psi rho Plus six a mu a mu Close to the bracket minus f times f bar You say a few words about it. This looks like I have a massive vector And that's precisely what it is But it doesn't couple to anything, but there is no gauge degree of freedom. How could it? How did it arise? Because this scalar field was charged under u1 And if it's charged under this u1, but I gauge fix it remember that The real part of it I gave an expectation value Yeah, our gauge fix it to a constant and of course in its kinetic term There is a d mu phi d mu phi covariant d mu So that's going to be an a mu a mu phi phi bar just like in the Higgs mechanism if you want So you gauge fix that and this term this term remains And this is just the ff bar term that you have for any of a chiral multiple of shell and in this particular case The eliminating it through this equation of motion is trivial Very good Are there any questions? Yes, yes Yes, yeah, that's right Are there any other questions? well, but that In this view you cannot do that because that's Against the equation of motion But yeah, you can I will do gauge supergravity later on that's one layer of complication after the other So you see here that this was the action that the on-shell action I wrote down before the equation of a mu is a mu equal zero So this whole exercise was pretty in some sense Well, you didn't gain much except that you have an off-shell formulation here. Okay So now uh, we repeat the same exercise now in a n equals two setting. So Um Let me first. Yes Oh the new minimal you start here with a tensor multiplet. So a tensor multiplet has what has a tensor multiplet has a tensor a real scalar and a fermion And now what you do is now you have a real scalar so you can only impose a gauge fixing condition on um On the on on on the real parts or the tensor remains And so then you're still left with the u1 symmetry. I cannot use it to gauge fix here So this mu really becomes a gauge field there and that's new minimal So all these old formalism the old minimal and new minimal they have a very natural interpretation Well, if you call this whole program natural, um a natural interpretation in terms of the super conformal method So the idea is make a bigger theory with more symmetry at compensators gauge fix and you get primary supergravity off-shell Only yes, uh, only if you go through this, uh Super conformal method. Well equivalents in the sense of um on shell you start to see that they become equivalent off-shell They use different compensators and then they become well classically they become equivalent I don't know what the status is about about the quantum theory. What are what are these these these? Differences show up. Maybe addition or something about it or somebody else So when you used to do rigid a super gravity to couple to some fields then the question is This is not completely quantum, but it's sort of something in between right you use a background an off-shell background to couple to For theory and the question is then again whether Um, I don't know what I understand the question. Um I don't know if the answer is known and if it is known. I don't know it Um, so I don't know I am absolutely sure the loop corrections have been studied in in in Both on shell or old minimal and new minimal, but I don't know what is the status of the art I I I think as far as people could judge they still lead to equivalent theories. Otherwise we this would have really been Emphasized more in the literature. I think yes, but maybe maybe some people in the audience know better Yes Well, there's not gauge invariant anymore. It's it's it's it has four degrees of freedom Um, so it's not it's not gauge invariant Well, it was gauge invariant in the theory where it was not gauge fixed But I gauge fixed the u1 and the dilatations such that Um, it is no longer gauge invariant. That's not a problem here because it doesn't couple to anything It doesn't give charge to anything and so it is just an auxiliary is just auxiliary here Or algebraic if you want. Well, I think it is the right way of saying it stuckelberg is uh before you do the gauge fixing Yeah, but not here anymore. Yeah, or maybe that's still called stuckelberg. Maybe it is. Yeah Okay, um, I have two minutes something um I just want for fun to um, say in two minutes the n equals two because now um Then we see what what will come to you tomorrow or no this afternoon So an n equals two super gravity It's just a simple remark that I will make here Well, we have of course two Gravitinos i equals one to two. That's what n equals two means And there's still only one metric Let's not worry about off shell off shell will come this afternoon So this had two degrees of freedom So on shell This had each gravitino on shell had two degrees of freedom It was this exercise that we didn't make here. There's 12 off shell But two on shell but now I have two of them. So that's four This one still has two so on shell. There's already a mismatch here. And so you have to compensate that or add another field That compensate for this and of course What immediately comes to your mind is an honest to god gauge fields Which in four dimensions has two on shell degrees of freedom And so now we have four plus two plus two That suggests already that n equals two supergravity at least without any matter couplings. This is called the gravity photon Because it's part of the gravity Multiplet that the minimal supergravity not coupled to any other matter Is just Einstein Maxwell Coupled to and then added to it. It's been three half particle And in Einstein Maxwell, of course, we have the reichner-nerston black hole and And we can start thinking about black holes and extremal and bps and so on But I think I should I should stop here and continue this afternoon. Thank you


What's going on guys? It's your boy DPJ here today with another Destiny video and today we have top 5 Sniper Plays of the week. Now if you guys do enjoy the video at the end if you could leave a like I would appreciate the support. Thanks for stopping by as always and so be any badass clip you've got to the email I'll just link to the top of the video description. Again, thanks for stopping by and I'll catch you guys on that next one Zone a lost three down. This is amazing No, not this time controlling those zones is the only path to victory This is amazing Your team is in the lead opponents down all enemies have been eliminated DPJ go and subscribe


Welcome back as we close out what has been a very feel-good Friday morning. Thank you so much for sticking around now when it comes To property and finding that dream home It isn't just about the house you like the image you have in your mind of what it should look like as they say It's all about location location location when it comes to finding your dream home That means the neighborhood you buy in is vital now Simon Bray CEO of private property is here to tell us more about an Incredibly interesting campaign the neighborhoods campaign Simon welcome to the show. Thank you so much So what's the hype all about I know you are particularly passionate about everything that you do But this seems to have kicked that into an entirely higher gear talk to us about the neighborhoods campaign This is an incredibly exciting release for us, you know, we've been keeping it under wraps for probably the last six months We've been working really hard behind the scenes Ultimately, we wanted to answer that question. What is it like to live in a particular area? You know, it's it's so much more than just the property you want to buy, you know That is something we've got on our website there thousands of homes for sale You can certainly find your perfect home, but we realized through our interaction with our customers They wanted to know, you know, what is it like to live in a particular neighborhood? What is that location all about life like around that coffee shops, you know little restaurants The property market what it's doing up or down So there's a lot of insight that we've got on the site that we just weren't making visible to people So we've worked really hard to kind of unearth all of that good stuff I was gonna say unearth is a good term because there must be a huge amount of data to assess and time We know that South Africa's property markets can be very regional and differ greatly from area to area What do we find what experience do get when we log on? Well, that's that's one of the cool things that we've done is we've taken property insights and and made useful visible Insights out of the data that we've got we obviously aggregate all of these thousands of listings on the site We've got database that goes, you know 10 15 years back So we can see a lot about the market and we wanted to make it obvious on the site So there's stuff like median house prices in an area. There's recent sales And and some great rental insight too, which is quite unique. Yeah, certainly from my perspective living here in Cape Town It's all about those rentals and of course all about those investment This says to me that this is a wonderful tool for people looking specifically on the investment line How does it help someone looking to to grow? You know that that asset and find the right kind of asset well a lot of investment is obviously buy to let so guys buying Apartments and then they want to let them out and when you do that you obviously want to pick an area where The rental yields are really high So any savvy investor could look at our site now look at a particular neighborhood and see the capital gains in the area So your sales price increases right next to the rental data So you can see what the rentals are doing what the average rental yields look like So if you're a savvy investor you can connect those two and that's novel. That's unique There's no other platform on the market right now. That's doing just that This all says to me that we're empowering ourselves. Yes through education But it just seems to have tools that really especially for a first-time buyer or someone who might not know the market You might be feeling like they're on the short end of that exchange working against agents who know so much more This really does feel like a tool to empower. How does it empower us as the consumer? We wanted to touch on it from a number of different angles. So there's obviously the information So it's the data that we spoke about It's it's something just as simple as when we talk about this neighborhood What suburbs are in that neighborhood? So we've got some rich mapping to kind of show what we're talking about when we mention an area And then there's something that I think is pretty unique You know something that we've worked on is this this original idea of lifestyle shopping for property You know, that's something that's emerging a lot of people are not just location based But they want to pick a particular lifestyle whether that's You know urban sophistication and kind of modern lock up and go lifestyle or perhaps it's you know You're getting older in life and you want to look at particular retirement lifestyles that suit you So what we've done is cross-classify all of these neighborhoods in the country and we and we've created these lifestyle tags Which is completely unique. So so there might be an area like Belito up in case it in that's similar to somewhere in Cape Town And now we've connected those two together on the site and gives you a different way to explore and then You know the one area that we wanted to promote as well as the side area of experience I mean I touched on it right at the beginning Exactly. I have to ask you and you know this question was coming. What is the best neighborhood in South Africa to live in? I know it must be a very very complex question Yeah, you know and that's probably what started a lot of our discussion initially is you know What is the best neighbor to live in and for each person? It's a different answer Yeah And so what we've created on the site is a discovery based platform and an exploration of all the different neighborhoods And you can choose for yourself exactly what the best neighborhood is. I love it open your eyes Well can quickly wrap up with what one tip from our buyers out there? Well when we talking neighborhoods, you've got to go and explore, you know you mentioned right at the beginning location is key and So what we're doing this Sunday is we've packaged three of our feature Neighborhoods and we're gonna be releasing them in the Sunday times They're gonna be on the site with these rich aerial showcases and like video footage. You've never seen before So my tip of the day would be certainly do your research find the lifestyle that suits you find your clicks Simon Thank you so much for joining us and congratulations look forward to what this yields But I know we're gonna be walking this journey with you over the next couple of months So I'm all the best of luck go out there and empower yourselves guys Make sure that you put some thought into the neighborhood that you and your family want to live in visit private property Dr. Kosa to discover more about private property and their new neighborhood information Sounds absolutely groundbreaking