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N = 4 Super YangMills Theory on the Coulomb Branch
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Title  N = 4 Super YangMills Theory on the Coulomb Branch 
Title of Series  Vadim Knizhnik Memorial Conference 
Number of Parts  12 
Author 
Schwarz, John

Contributors 
Belavin, Alexander (Organization)

License 
CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  10.5446/16987 
Publisher  Institut des Hautes Études Scientifiques (IHÉS) 
Release Date  2013 
Language  English 
Content Metadata
Subject Area  Mathematics 
Abstract  I will present a conjecture relating the worldvolume action of a D3brane in an AdS5 X S5 background to the effective action of N = 4 Super YangMills Theory on the Coulomb branch. 
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00:15
so I a better child more informative titles from going to say we would brains in the 2 cities states and conformal field theories on the cool breeze and what I plan to do is to preserve a world volume action for certain P brings an end to the space and return to interpret the results as an effective action 1st super conformal field theory on the Cologne branch the the principle of guiding me In doing this is to is to follow a principle that had been espousing others for a long time which is to take coincidences seriously there are several examples recent history theoretical physics where this has been a fruitful thing to do and there are other examples where there were missed opportunities because people didn't take advantage of this principle which we know and recognize the wisdom of hindsight so far so in certain cases I will boldly conjecture that the P. brain action is the exact effective action for the super control through Veronica Longbridge capturing entire theory Columbus and call it highly effective action exactly what is being trajectory should become clearer as we proceed so the discusses them with lots of supersymmetry were more mathematical control these systems which from the point of view of the previous talk would have been regarded as trivial because he was dealing with systems less much sediment supersymmetry ask more difficult question or we of all year but by the same token that means if may pages they had to make a stronger conjecture so the examples that can be discussed our D 3 brains and entered acidified times as far as the basic example of the idiocy of the duality I began to break 80 for 7 months up by sickly group seeking the deeds to rein in Haiti has 4 times the EP3 these 2 examples are both related to what's known as a J and theory which is a super conformal Chen Siemens theory in 3 dimensions and then there's a little bit maybe about the implied bring sentences for which is related to this mysterious 2 0 supra control field these actions so what I wanted to discuss probe the the world actions probe brains and in these geometries and his probe brains actions involve various wellknown approximation so there's the probe approximation which involves neglecting the back reaction the brain on the geometry and the other background fails since the brain as a source for 1 unit of flax and it's in a background of any of the flight neglecting its effect is closely related to ending large we are also pleased the brain actions are going to involve born felt like terms that's a function of the U 1 gage field it all the formula and born involved has no derivatives deals the filter itself so it's customary to say that this requires assuming that the field strength is slowly varying derivatives can be neglected so these are wellknown approximations associated with probe brain theories that despite all the formulas for .period actions have some beautiful exact properties they precisely realize the summitry the background as a world volume super conformal signature which in the case of the D 3 Braidwood hasn't to come to slash 4 on the ABC I'm examples of the OSP 6 last fall now in the form of going to be showing you have only looked at the Bozanic degrees of freedom I haven't put in the firm this is technically challenging but straightforward and it would just take much time postponed but so that means I will only supersonic subgroups of the Super these brain actions also implement the duality cemeteries of the background theories as duality so for example and sell exact symmetry of type to be superstrength and since the D 3 Bahrainis living in the background of that and the 3 Rangers invariant under wrestle to this group has to show up so as a duality Group of the brain probe action and there's a duality that turns out to relate the D 2 and 2 examples as well which discussed so the brain world actions have local cemeteries they have general coordinator variants this is familiar with all brain stories that starting with the number of Goto formula for straying where are you going repair Asian during formula and right on the area of of the World XI with which is depend on you parameter growth and generalized always brings to these actions at general cordoned various and has something of a local Kapustin but that's only becomes relevant when include pheromones and commuters riding for the purposes of making contact with effective actions that I'm interested in all natural gage choice in discussing these brain actions and that's called static and fatigue and this results in formulas after you make this case shows that have expected you can't afford effective action however the modifies the formula for the global symmetry transformations so I said the super conformal Group is a global symmetry of the worldwide and the formulas for how those that cemeteries realizes very straightforward indicating very formulation but want to go to static gage on the former become much more complicated because you have to include compensating gage transformations that preserve the Gage Street and this will be illustrated interpreted more so let's talk now about super conformal field theories on the school grounds so forget brain actions throughout all this very specific to start with and will have a couple more examples so let's discuss the example of a nickel for difficult for supranational with you to gage for most purposes like it's a free you on multiple at the couple's leaving initiative however decouple the yuan is actually necessary for the period have still to duality so all are not strictly speaking truth that you can ignore all that's been clarified by somebody collaborators recently exactly how it all works so with this caveat I'm going to speak about you too but I know of and on the Columba always just as Sampson was saying we have of the 3 supermodel was the makeup as you to always have 1 ,comma supermodel but there remains necessary :colon branched into called the abuse supra multiples that require a amassed when you're on the Columbus which no
08:01
principle 1 can integrate out the massive feels thereby producing a very complicated formula in terms of the massive voter supermodel but only the resulting effective action would capture the entire theory can be valid on the Columba regional energy may not mean may be the most useful form a very high energy that's all so this defines what I'm calling a highly effective action as the result of doing it's impossible calculation obviously we can't do this calculation however in some cases we know many of the properties the answer should possess so what the general requirements it should have all the unbroken and spontaneously broken global symmetries of the original :colon branch that so informal cemetery across spontaneously broken just because branch but it's despite being spontaneously broken it's only broken because the design of a therefore it has to do with choice of out of the action equations of motion of exact an exact symmetry about it should have the same duality properties of the cool branch theory explicit officials it should have the same BPS spectrum so what does that mean you only see the mass multiple you know in the formulas with the W you can find multiple solutions such as Florida and so what what I'm going to argue is that the but this election should have solid and they give all massive fuel but not only Vermont holding back environment but also the W themselves should be period of giving incomplete as well to multiple of so the claim
09:58
is that the probe appearing can start construction which is an approximate solution to the problem of purports to address there is a compelling candidate for the In a few special cases so these places include an equal for difficult for superior theory with you to gage an equal 6 days 3 ABT and theory with you to level times you to level minus can gage symmetry subscripts being the levels of transcendence note that were using gravitational theories of restraint period and as a tool for studying nonGM but our goal here is to say something benign gravitation and of course mark is that these 9 gravitational theories are going to have general course I think that's the the fundamental importance India mental conformal field there every tournament action must be mentioned that there's no dimension fullscale problem on the Cologne branch there's a scale which is the level of scalar field but as I said it doesn't need to be specified when you write down the action and so the full cemeteries realized on the action and the equations of motion and only the choice of accurate cemetery and in fact all choices could also really had just 2 discrete choices the vary around the pool branches are not good and I'm only discussed the long looking about half of the problem so the only unusual feature effective action is taken pains in various parts of and so individual terms in the action can arbitrarily complicated with more and more fuel than derivatives 1 but end up with the mentioned decently by including an appropriate inverse powers in the field this is well known to most people but this if you haven't thought about effective actions before so now since I wanna working ADS space set aside a little bit about so it's very similar from factory down except promoters and stability of India and I started to work in 80 s P plus 2 because I but he brings and the formula used my hyper surfaces just like the ones that example wideout what Lawrence so it was 1 time and peace spatial directions and you 1 time 1 space some 41 and so that that's formula has a soapy ,comma too cemetery and and the corresponding matches is just the thing and sewage it's just like the simple things are going to act when dividing up the from and solving this equation for years and substituting magic here this formula for the potpourri patch magic and the only thing that's not manifest in this farming on the conformal symmetry and that's trivial and the hyper surface is just some trivial transformation which eventually easily traced through this form analysis of the D 3 brain areas buttons 5 of the 10 dimensional metric is just induced for montages showed you answer on so it the 1st 2 terms at the top there are just the destiny of the magic for 5 sphere and so the tournament so much can all we can by doing using a standard trick which is detected Iomega fires were put the square in the numerator and the spirit the nominee and and you see that you have an odd 6 and is written in spherical coordinates and just recast you couldn't spaces to get this formula I'm not going to take interpretation that acts as the dimensions of life and he has the dimensions of mass and the end this is going to be identified as the Steelers field that gets the bottom expectations in the 3rd but it will be normalized very nicely as a stands allow myself to constant and rename it for so this is just a fudge factor to get the normalization 1 of the standard formulas and enabling the immediacy of the business relations between the radius Our Camelot and the string coupling constant the number of units of Flaxton strangling scale and then there's the there's a 5 form flock that spreads the fire sphere which is proportional and the number units of flocks in the coefficient just depends on the convention and the actions
15:00
that 1 has for all brain is the sum of 2 terms which I'd like to call this 1 to all too often people as 1 DDI for standing for direct warning felt and as to the destined for returned Siemens but you could attach many other names to each them as well so I prefer to go on this 1 that's 1 is does have a direct warning of structure and that's the end of function involving functions that charges would tell you so some of the parameters of the world I am of the brain and acts as the spacetime I just tells you how the brain is embedded in the space that's what I called betting functions and in addition would you always have talking about the brains is the world you engage field which is a vector field on the brain so it has no space index before you do gage fixing it completely and the entire supra control so it only gets a transformational after we it doesn't transform it all before and has the feel you won't feel free to everything I'm doing billion a single brain relatively easy so here's the standard formula for the balls on the part of the section she is the and is again as the pullback of magic to the world but just yet again after Prime is registered local registrar of slope which is the square of the stream like scale and so I wrote that up in the upper
16:41
corners of prime related scale is a form of attention of the D 3 brain which is standard stuff it has its bps so the former completely exacted an ambiguous and combining equations the things which combinations that ultimately appear equations on 4th times into part of a plan to buy back good and those are just pure numbers so all scales dropout of the problem so there are no dimension phone numbers in this section now I know we can delegations to the standard gage simply says taperecorded cycle that new and identify them with the world of course that's start gage that tells you exactly where the brings local but the attack in an certain mentions that the other the other fields the words we will review were located in the radial direction from the 80 s and its position on the flights embedded the 6 scalar fields and then gage the 6 scalar fields and the he'll become functions of actors replaced by so we now have this
17:57
formula and I like that all the numerical coefficient in writing just would fit on the slide but later on give for a withdrawal the versions are dimension lessened only functions string coupling constant and the number of units of remarkable what has happened to the finalization of the coefficients of but when I do show cooperation you'll see that this formula is 1 of a string coupling constant time expression only involves isn't combination Gstring times this fact I think is interesting because it suggests that the loop expansion of the the interpret the thing is what I'm calling each year a highly effective action and this suggests that the loop expansion corresponds to the topological expansion of the 9 billion so so the classical HEA action winning told the entire planet theory of this is correct so entry approximation this means should exhibit dual conformal symmetry unions amateur like that hasn't been demonstrated in Prague to fall that this would be true so so I should say that the act this like everything I'm doing is conjectural that this has anything to do with this each year is a conjecture because you could imagine that is another former has altered the properties and this is the wrong 1 of we right but as you will see I don't have a good interpretation of parameter N N making this argument I'm assuming that enters the usual and were familiar with and so there's a practice this part of the discussion is accused secondary conjecture that could be false even the first one is I will have to discuss what I do with because what I'm going to find is that I don't get a unique theory with all these properties I get theory label by managers and and I only want 1 for me so what I'm going to do is put an equal to 1 that's the only natural choice which is kind of remarkable from the program .period you because that's where the approximation is worst Sony remarkable under induced transformations said so on devoted about Monica and a standard gage with fixed with X is it's been related decisions and so if we have some of the transformation of acts as part of our super conformal group under which exchanges I have had a general coordinator is to bring the change total change back to 0 so that's that's the compensating gage transformation to stay in the standard gage and that general coordinator and then faxed the transformation rules the other fields in the theory when Fuhrman's included is also local capital which also has to be gaged fixed and the compensating local capital cancelations will give rise to complicated supersymmetry transformations that supersymmetry transformation will be easy before you gage fixed but that we very complicated attitude and these extra contributions will can be interpreted as quantum corrections due to massive fuel for an integrated out people have tried to construct effective actions order by order but what I got bruteforce using the method herself and find that the keep modifying supersymmetry formulas transformation from as they do it so it's kind of organizing principle for her supposed to go so when they come to a 2nd term in the action as the transcends time this particular example of the 2 pieces that the Ramon Ramon for forms for that has to be integrated over the world I am and if you want you can have a sees 0 which is a Ramon Ramon 0 form which is like an axial and its expectation values high which is something like a faded so there moments for form has itself still feel threatened and there can be written down explicitly if the volume 5 4 5 0 plus the bottom 5 4 of the suspects that's manifestly self rule don't think said is the expectation of 0 0 in the back it occurred across that the topological tournament doesn't contributed classical equations of motion the asked 1 remembered as 1 of the spirit of tournament and that determine thing inside the determines that a gate started out with a new plan of about fields to expand that determines the series field start to what no 1 multiplies fighter force so that 1 contributes With socalled potential to fight for the 4 x which if it were there would be a disaster because it means a force on the brain and we know that thing is bps and the forces of got a canceled like much of this term has to be canceled 1 discusses this in his original famous paper with over 9 thousand citations and it says exactly the right thing which is that you there must be a minus1 added that determine so that this the parts potential is not the sort of thing is that the small contributions made is to evaluate the contributions for angelic against precisely the right answer with the current coefficient the complete answer aside from Vermont this the Brennan is given by the and here I show all the coefficients Selanne Gstring times all I can already explained and then there is the only way announce that the alliance consistent with that in your eyes are so so there's still failed because the case is still to come here after and so that's the the Bozanic part of the formula so so farmers if the conjectures writers from should already be of some interest because it which you will get from the complete answer when you because of the so soon you can see 5 4 has been canceled minus 1 so someone to the issue of SQL so we introduce a model parameters which is talentless I tend to to real party wanted is what I was going what is called time out there and have to 1 over Gstring which appears on the front there inside glimpse workers remember Maryland Gstring Tenzin but I'm going to put an equal to 1 eventually so as to serve in
25:33
the manuscript that I will post after I get back from the complete proof of the estuary of the formula is shot given but I'm going to give you a simplified version right home at the scalar fields some of which would be the flavor of the argument but it's not complete as it stands so far so if it might take the form showed you and throw away all the scalar fields on any something I would like that and I were dealt with and you can support terminal in candle narratives that's well known in many places in literature on the next to analyze the excels in the estuary which act as an independent field and grandmother quieter that implements the fact that that is the status the and multiplier form I wage and who's got quite emotions tells that is beyond and inquiries emotioncharged DH 0 to set the making the exterior derivative the dual potential the and then you have the F equation motion sobering happen this time due to duel and in the terror and blasted the formula isn't complicated expression which is here so this comes from the topological term and this comes from the determine justified differences with respect unit now to demonstrate estuary where you need to do is to solve this equation for S In terms of you can see that look like difficult algebra the amazing thing is develop In the answer Is is that have to go
27:30
over the same function age Intel prom With help from minus 1 and so that means that there is a dual action here which gives all the same set of equations and so so that so that is the duality on and I I have worked it out with the skill the nominee turned to so the 2nd example the candidate for to levitate I'm here to play might escape ABC and the political branch so a medium there is less of an eagle Sexton Siemens there treated with his office and plucked super and then we can have this problem from 2 directions so the 1st directionally discussed and to bring in 80 years 4 times 7 so this is the same as the this action has the feel content and structure of the 1 level Kate you 1 level minus ABG so that's what you expect on the :colon branch everything else is an integrated at the deed to bring some stressed the media's 4 times EP3 and this action turns up the content and structure of billion threedimensional an eagle 6 Supreme animals Sutherland theory has it still feels various still feel that you engaged but you engage Hill is related by duality was still fielding 3 so they're going to turn out to be a problem all the calculations show you carried out for any flights but before injecting a 1 is the role of interest so for them to bring their of recovery the corner the 7 Corners combined into 4 dimensions so we want them to have a scalar fields winner in 3 dimensions and so these Pfizer have dimension half from the mentioned 1 when they were in 3 dimensions and so on so that the analog formula showed you before but now we have to move into the building and this money out of his by the case of the sphere the way that's done is that the the covert derivatives and so far are for complex still feels rather than real ones when wanted and we are so we have all the answers you engage skills so that they had charge 1 minus 1 in this way and we want a building today the requirement that the it's actually the gradient of the still feels listed derivative still field and that the scalar field is periodically period to private this was that if that's the case then this will be an equivalent on the still feels now represent money out but as you can and some of the the wayward is by having a giant Siemens turned the ensures that there is a problem and that so other small changes compared to the standard formulas but the former defined in the region paper where were the rate regulation register as a sex factor of K and the formula for the conversation the flights and it is the only way to get out over the modern space 2 years so of the farmers of their so the analysis
31:25
is similar to the fore again at the end of the monolog reform that provides the crucial term had this crucial minus 1 cancel the 1 from the determinants of no force acting on the brain and so in this case we can define of parameter and overcame the standard choice she also find paper and written in that language that before the final answer I obtained from and there's plenty here is the formula shown here were destroyed and 1 love it can't get worse an oral care and the function of land so again if you take the independence of the formula seriously but again there is this idea that you're going to get the full union Cemetery in the tree approximation here is the chance an instrument of this for a grandmother it tells you that this is a great deal of scale and the coefficients things properly tells you that skill period to put the case this term can be written some of the differences to Tristan chat turned Simon terms by taking the sum and difference of a and B and then you can use a viewing times you mind structural somebody to bring on the people of the semester the magic of simply against policy scale out of a house in compliance with the peace treaty in and the 20 thousand dimensional space written this way this looks like it has a scalar fields but there's actually a local U are really 7 of them
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and the pullback of the magic to the treatment of the 2 brand worldwide action all of this is denoted by but I described as 1 and end to terminus case has 2 pieces 1 is integral to the world as a whole or cancel the 1 from the German salt and there's a 2nd term because as a medium already noted there's also a remote from 1 form In this construction on which contributes an amount that can be written this way so that were 4 patterns W it's basically the same 1 in the background value of the 1 which is substituted in former standard formula which is the 1 where and dumping is given by this formula in terms of the complex scalar fields and the geometric interpretation is the double uses the the C P 3 killer form the putting these ingredients together to complete the 2 in action aside from firm the demand for so here are all the genes which event from previous floods in corporate this and other and the and the you engage this so that when we got here by the time we get to stand against this I the feel content of supreme Mills theory in 3 dimensions it's surprising that you would find that the theory that has no skill this is the 1 about the Kennedy chairman in a Alaska has the wrong we don't get the intergalactic scurry to get the integral 5 minus 2 times of scoring which has dimensions 3 so by manipulations vary somewhat approve of throughout the 3 1 can demonstrate that this is equivalent To the 1 I got from the answer sometimes people think that the tight to a picture less powerful than 11 actual picture but here you reproduce the same promise but there is 1 piece of information you don't know if you only do it for the 2 appointees is actually writing of cash Carroll and what the parameters that you have when you do that to a problem Gstring and then you don't have a cat and it turns out that you what you don't know if you only knew the 2 histories and know that this is the former Virginia in terms of an income CGS is not a continuous parameter in this problem it depends on 2 images In this way when if you only knew tied to a string theory you would know that but otherwise the 2 from the club so I only have 1 flight others and vibrant a very quick the and the Canadian 7 times that's for unfortunately is no analog of mining operations and because of that everyone will get here doesn't have a small parameter in and doesn't have a perturbation expansion of finding a classical formula for a theory without a small parameter as a questionable value but I think it's 0 value but it's not as much value as you might like the case if you do it here steps attorney has that their foreign to our by the standard trick and in the end Madison songanddance you end up with this formula just like before were aged his aides straddled the news is a complicated story for how you represent itself due to form itself freeform so far in the center of theory and that is discussed in papers profit in the 90's but I don't want you here the case has that information and so and again was His only 1 parameter and and I want to identical to 1 and initially and I'm enjoying coefficients sir I should emphasize something that even even notices this the classical approximation to theory that doesn't have a small parameter it's nonetheless interesting because the the corresponding foreign unbroken gage symmetry doesn't exist but there is no analog wanted to gage before the 2 0 so even now it's not a terribly useful for me police said I think that's already progress and I think it might be useful for studying solid and so there's the thing should have a self dual string of solid and I think that suspects BPS maybe this is good enough for doing this so what the motivations for my doing this work was to understand the 2 0 formal filters and 6 dimensions on the and some of the implied reaction to show that is a good team and candidate for the simplest such once but as I just said its applications are limited because it doesn't have a small profit on which to base a perturbation expansion the besides looking for solid that's another thing that might be it might be good for it is if you if you compact about a circle or a Taurus something you might introduce additional parameters of that July discussed some limits on which is weakly couples all of course when you do that you're going to be breaking the conformal cemetery explicitly and I'm a little uneasy about that and as already said there is no known Lagrangian formulation in the unbroken and 1 and it's widely believed that 1 doesn't exist that makes this significant perhaps so relaxed so all this is because obviously very speculative the reasons behind him but I'm sticking my neck out saying that the speculation should be taken seriously is because systems have so much symmetry that I think that's very constraining so that there is that large super conformal group duality the solid which haven't yet been constructed but I'm confident that the if if these if the dual conformal symmetry of the tree approximation is demonstrated of possible approximation that would be very encouraging all I know about what it wants to do all the things that as for the 1st 1 of the important thing the cost incorporate Vermont and that technically somewhat challenging that and this question can be done and I know how to do it analogously flat spaces or harder in India space but when we have that we all want to compare expansions of these formulas with the results for Cologne branch lowenergy effective actions because people by brute force several terms in the suspensions of most of these theories and so obviously compare it's clear they were very carefully because they didn't discover that there is freedom in any form are so big of people who write down these expansions using method missed the fact that is freedom of nature In carrying out the comparisons the various things that might look wrong at 1st they might have terms that involve more derivatives of the field of action his remember I know food no derivatives of death in the formulation of 2nd derivative of flies but they're also the possibilities for how that might get sorted out if such discrepancies were to appear on the possibility of definitions which could shift around the number of directors forth and also Sampson went out to yesterday is also the freedom that we just adding total derivatives the formula or which goes to a partial integration always which can also shipped derivatives so Interpol these things together you wouldn't you would have to take those possibilities into account into making comparisons with existing forms literature so I think interesting to explore soliton solutions of these things all and explore so if if if they think this Union symmetry the formula for tree approximation scattering amplitude should have some very pretty properties and so I think you'd be interesting to indicated them explicitly and with all the time technical tools that exist out there the people really well equipped to do that and not 1 of them but I think may may turn out to be a good problem we want to understand the extent to which cemetery and other general considerations should determine the line to make the case more compelling and I'm not exactly sure how to get a handle on ah but this holds off as people examined if if if if people decide isn't completely crazy the 1st 1 will become bolder and stronger conjecture that he supplied the systems unless images and so on and so forth all and other obvious questions you'd like to generalize even with this much supersymmetry like a generalized hiring cases so that you to you like to do is to 3 which had to go viewing multiple it's rather than 1 this means that the I found the former arbitrary integer n them above those of the foreigners should have an application so I think those formulas will play a role In answering these type of questions but I doubt that they will enable you to write down the plant I think they'll be terms in the formula that involved these things with various but that there may be an additional terms which is much more complicated really I'm a little worried that I might turn out to be a real once 1 has a good understanding of classical theory and an instant makes sense 101 understand its condensation looping so we agreed on all massive stuff but you still have the interval of masses and again at the confront although and this the former as a general coordinator in some local capital cemeteries in view of the gage fixing goes mirrors the World War and II so this slightly interesting and furthermore that infrared divergences when you start integrating so that the possibility services going to be challenging but I think it's analogous to the things that people don't know the setting sun sure that people have the requisite tools I like can conclude by saying we conjectured that the world climax a probe brain and the maximally supersymmetric threequarters maximally supersymmetric spacetime with into the city it is said can be reinterpreted as well I'm calling a highly effective action of super conformal field theory and plusone dimensions :colon branch and the main evidence that the actions incorporate all required cemeteries and duality which in the case of the D 3 Verano supergroup to for when the parameters included an insult to the duality and verification of dual controls cemetery with string .period I think it might be interested do you on the line Hi action week will problematical it seems that the current he defined by grave doubts about that loss rather than on the issues of mutual displays are faceoff .period for you know you can will use of local but lovable has arbitrarily many derivatives exist not higher demand during many the 1st derivatives of arbitrary powers of outsiders that's local of its was seriously where there but I tried to do that when I said that it appears solid just like your multiple this year the theory has as I demonstrate has the to the cemetery to have 1 of the up assault on the other ones assault How can we used to be integrated into and what you see is what you see is you what will I said that's impossible by conjecture and on the way forward well I'm congestion exact answer your that this but I think from going the road down is better than anyone ever dreamed but it has the general cordon variants has the cell to the duality and I think the fact that they didn't put in the harder about a few tries and tries to maintain the General Court over it's not so easy and are still to be far side of the multiples of the past but this is the case in Boston internationally and so on and so on all this and it will be at the back of the head of the he also eliminated them address them that thing inside the terminal In principle the what's been shown in states have investigated here is that in the limo advantages the energy goes to infinity here so that she wouldn't get there you like like in relatively and the intent considered as would be analogous another thing I remarked is that if you go if you in eyes which you would need to do for Canada then the thing inside the group is positive that's obvious to the government to think of that to see that that's true that I think is encouraging but he has been mailed to all of you have to do with you can you break down the forests and challenging the 2 of them are all the things that people written down although I haven't made try and tried to make detailed comparisons but they're the same general appearance protruding from the 1st 2 terms over year well we will only if they got into Nevada and he finally got to the front of number and if they do find higher derivatives that also the possibilities for getting rid of them as was mentioned most recently during the selection of a fugitive from justice and his vegetables various castle built in that's right that some of the things you worry about the sort of guarantee best amateur nothing I worried about for a little while where if this is the 1 over an expansion and putting an eagle the 1 that doesn't sound very good for the expansion but you have to look at the former more carefully because there's still a couple of times and then you know that the 30 stocks weakly couples so I think that's OK this year and is known for crime for you to have the sole well all you do is talking about that by doing all the animals by doing the past this is the part expansion of years yeah that's I said that I haven't tried to compare because much of the aim some of more interesting to the founded the fermions like this side of the paper over 5 all I know that that's known to be present because so is interesting that there a term like that without new derivatives in and only starting inside the and even tho I haven't done the firm look at enough to know there will be a term of that general but because the left in the season goes resentment explored so I haven't tried a detailed comparison of the answers I have tried to use the facilities for the rest of the year with the people who do these things by new method find answers so far so much they made a mistake got agree with for some guy that that might be enabled to confirm my speculation has won it might realize that the inadvertently put an equal 1 right now recognize the possibility that it said
00:00
Axiom of choice
Group action
State of matter
Multiplication sign
Conformal group
Cohen's kappa
Derivation (linguistics)
Duality (mathematics)
Local ring
Physical system
Spacetime
Coordinate system
Physicalism
Mereology
Bilinear form
Functional (mathematics)
Entire function
Flow separation
Category of being
Symmetry (physics)
Hausdorff dimension
Duality (mathematics)
Natural number
Conformal field theory
Right angle
Conformal map
Resultant
Directed graph
Geometry
Point (geometry)
Transformation (genetics)
Metric tensor
Theory
Number
Frequency
Degrees of freedom (physics and chemistry)
Wellformed formula
Term (mathematics)
Natural number
Field (mathematics)
Units of measurement
Multiplication
Gauge theory
Quadratic form
Subgroup
Approximation
Supersymmetry
Commutator
Invariant (mathematics)
Units of measurement
Weltlinie
07:59
Axiom of choice
Group action
Multiplication sign
Direction (geometry)
1 (number)
Mereology
Food energy
Expected value
Derivation (linguistics)
Duality (mathematics)
Scalar field
Gravitation
Square number
Hausdorff dimension
Effektive Wirkung
Area
Theory of relativity
Spacetime
Mass
Inverse element
String theory
Term (mathematics)
Bilinear form
Metric tensor
Category of being
Numeral (linguistics)
Wellformed formula
Symmetry (physics)
Hausdorff dimension
Approximation
Duality (mathematics)
Equation
Normal (geometry)
Energy level
Spontaneous symmetry breaking
Conformal map
Resultant
Fundamental theorem of algebra
Length
Flock (web browser)
Conformal map
Divisor
Transformation (genetics)
Tournament (medieval)
String theory
Mass
Vector potential
Metric tensor
Theory
Number
Power (physics)
Frequency
Thermodynamisches System
Equations of motion
Wellformed formula
Term (mathematics)
Radius
Symmetry (physics)
Energy level
Equation
Field (mathematics)
Units of measurement
Newton's law of universal gravitation
Scale (map)
Addition
Multiplication
Axiom of choice
Scaling (geometry)
Sine
Surface
Mathematical analysis
Theory
Gauge theory
Group action
Sphere
Power (physics)
Calculation
Voting
Radius
Scalar field
Lie group
Autoregressive conditional heteroskedasticity
Factory (trading post)
Field (mathematics)
Gravitation
Fiber bundle
Coefficient
Units of measurement
Vacuum
Spectrum (functional analysis)
Matching (graph theory)
14:57
Mass flow rate
Direction (geometry)
Multiplication sign
Sheaf (mathematics)
Volume (thermodynamics)
Parameter (computer programming)
Functional (mathematics)
Mereology
Metric tensor
Number
Prime ideal
4 (number)
Invariant (mathematics)
Wellformed formula
Term (mathematics)
Scalar field
Symmetry (physics)
Square number
Statistics
Equation
Field (mathematics)
Position operator
Addition
Scaling (geometry)
Spacetime
Algebraic structure
Price index
Gauge theory
Functional (mathematics)
Bilinear form
Entire function
Summation
Fluid statics
Vector field
Function (mathematics)
Hausdorff dimension
Combinatory logic
Equation
Local ring
Spacetime
17:54
Axiom of choice
Group action
Correspondence (mathematics)
Thermal expansion
Conformal group
Cohen's kappa
Kopplungskonstante
Expected value
Summation
Local ring
Multiplication
Proof theory
Coordinate system
Parameter (computer programming)
Category of being
Radical (chemistry)
Symmetry (physics)
Duality (mathematics)
Order (biology)
Determinant
Slide rule
Transformation (genetics)
Tournament (medieval)
Approximation
Subgroup
Rule of inference
Number
Goodness of fit
Coefficient
Thetafunktion
Numerical analysis
Term (mathematics)
Equation
Quantum
Units of measurement
Exterior derivative
Series (mathematics)
Theory
Independence (probability theory)
Volume (thermodynamics)
Total S.A.
Mathematical model
Group action
Gauge theory
Vector potential
Supersymmetry
Loop (music)
Function (mathematics)
Network topology
Force
Euler angles
Multiplication sign
Decision theory
Firstorder logic
Angle
Parameter (computer programming)
Mereology
Independence (probability theory)
Duality (mathematics)
Mathematics
Manysorted logic
Scalar field
Determinant
Moment (mathematics)
Ext functor
Thermal expansion
String theory
Term (mathematics)
Bilinear form
Functional (mathematics)
Entire function
Proof theory
Fluid statics
Hausdorff dimension
Equation
Quantum
Hill differential equation
Right angle
Conformal map
Classical physics
Computer programming
Topology
Conformal map
Modulform
Vector potential
Hand fan
Theory
Equations of motion
Network topology
Wellformed formula
Symmetry (physics)
Field (mathematics)
Subtraction
Loop (music)
Multiplication sign
Multiplication
Forcing (mathematics)
Consistency
Expression
Weight
Transformation (genetics)
Approximation
Computer animation
Combinatory logic
Coefficient
Local ring
27:28
Axiom of choice
Complex (psychology)
Spacetime
Building
Group action
Direction (geometry)
Multiplication sign
Strut
1 (number)
Dimensional analysis
Summation
Derivation (linguistics)
Duality (mathematics)
Mathematics
Scalar field
Analogy
Hausdorff dimension
Determinant
Geometry
Spacetime
Regulator gene
Gradient
Complex (psychology)
Term (mathematics)
Functional (mathematics)
Wellformed formula
Frequency
Hausdorff dimension
Duality (mathematics)
Equation
RWE Dea
Condition number
Convex hull
Length
Determinant
Set (mathematics)
Algebraic structure
Calculation
Modulform
Mathematical analysis
Content (media)
Coordinate system
Discrete element method
Shift operator
Metric tensor
Theory
Frequency
Wellformed formula
Term (mathematics)
Radius
Symmetry (physics)
Quotient
Energy level
Equation
Subtraction
Scaling (geometry)
Sine
Forcing (mathematics)
Content (media)
Mathematical analysis
Theory
Algebraic structure
Independence (probability theory)
Set (mathematics)
Mortality rate
Group action
Transformation (genetics)
Sphere
Approximation
Similarity (geometry)
Calculation
Summation
Network topology
Coefficient
Units of measurement
33:28
Complex (psychology)
Spacetime
Group action
Confidence interval
INTEGRAL
State of matter
Correspondence (mathematics)
Multiplication sign
1 (number)
Insertion loss
Conformal group
Solid geometry
Parameter (computer programming)
Mereology
Food energy
Derivation (linguistics)
Duality (mathematics)
Connected space
Manysorted logic
Analogy
Forest
Scalar field
Circle
Physical system
Spacetime
Supergroup (music)
Coordinate system
Thermal expansion
Perturbation theory
String theory
Term (mathematics)
Bilinear form
Flow separation
Radical (chemistry)
Symmetry (physics)
Hausdorff dimension
Duality (mathematics)
Conformal field theory
Resultant
Length
Determinant
Field (mathematics)
Filter <Stochastik>
Suspension (chemistry)
Classical physics
Modulform
Mass
Event horizon
Theory
Number
Power (physics)
Frequency
Goodness of fit
Coefficient
Wellformed formula
Term (mathematics)
Natural number
Divergence
Selectivity (electronic)
Integer
Field (mathematics)
Condensation
Pairwise comparison
Multiplication
Sine
Forcing (mathematics)
Minkowski space
Content (media)
Line (geometry)
Group action
Limit (category theory)
Cartesian coordinate system
Approximation
Supersymmetry
Field extension
Network topology
Coefficient
Discrepancy theory
Local ring