tag:blogger.com,1999:blog-8883034.post113016393724746757..comments2024-08-24T00:41:35.396+02:00Comments on atdotde: Hamburg summaryRoberthttp://www.blogger.com/profile/06634377111195468947noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-8883034.post-1130499488229800452005-10-28T13:38:00.000+02:002005-10-28T13:38:00.000+02:00Yes, see also Jacques' latest postYes, see also Jacques' <A HREF="http://golem.ph.utexas.edu/~distler/blog/archives/000664.html" REL="nofollow">latest post</A>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-1130496484399419432005-10-28T12:48:00.000+02:002005-10-28T12:48:00.000+02:00Giuseppe gave me the hint that Nikita's talk is cl...Giuseppe gave me the hint that Nikita's talk is closely related to Witten's latest paper which I started to read on the plane to Cambridge (I am currently in a cafe at Stansted airport).Roberthttps://www.blogger.com/profile/06634377111195468947noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-1130496168662278582005-10-28T12:42:00.000+02:002005-10-28T12:42:00.000+02:00I'd have one more comment.Robert wrote:"Nikita arg...I'd have one more comment.<BR/><BR/>Robert wrote:<BR/><BR/>"Nikita argued [...] that this requires the first two Chern classes to vanish."<BR/><BR/>I have begun looking at some literature on this, which in particular goes under the keyword "chiral deRham algebra" or "chiral deRham complex". This is a sheaf of conformal superalgebras on some variety X.<BR/><BR/>There is something closely related, namely a sheaf of graded vertex algebras, also called a "chiral structure sheaf".<BR/><BR/>While the chiral deRham complex exists for arbitrary X, the chiral structure sheaf is apparently well known to be obstructed by the second Chern class of X. <BR/><BR/>Moreover, it is apparently well known that the existence of a globally defined Virasoro field (stress-energy tensor) in this context is precisely obstructed by the first Chern class of X.<BR/><BR/>I don't know if Nikita Nekrasov is aware of this, but it sure seems as if he deals with a special case of this general theorem.<BR/><BR/>This is discussed for instance in <BR/><BR/>Gorbunov, Malikov, Schechtmann: "Gerbes of chiral differential operators I, II, III", math.AG/9906117, math.AG/0003170, math.AG/0005201 .<BR/><BR/>See right the first page of part I.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-1130263212131521732005-10-25T20:00:00.000+02:002005-10-25T20:00:00.000+02:00The talk by Hitchin is already online. I guess all...The talk by Hitchin is already <A HREF="http://web203.ownspace.de/zmp/frame.php?lg=en&sheet=events&subsheet=opening" REL="nofollow">online</A>. <BR/><BR/>I guess all speakers have been asked to provide transparancies, which should appear on that site.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-1130260547442231672005-10-25T19:15:00.000+02:002005-10-25T19:15:00.000+02:00Thank you for a very nice summary. It seems like a...Thank you for a very nice summary. It seems like a fun conference. Do you know if the talks will be available online?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-1130249077866218292005-10-25T16:04:00.000+02:002005-10-25T16:04:00.000+02:00Got me, one 'not' too much. Of course nothing that...Got me, one 'not' too much. Of course nothing that diverges fits the axioms. If your perturbative expansion does not converge it does not really define what you mean by your theory so there is nothing concrete that you could even envision to check the axioms agains.Roberthttps://www.blogger.com/profile/06634377111195468947noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-1130167976387006862005-10-24T17:32:00.000+02:002005-10-24T17:32:00.000+02:00"And perturbative descriptions on terms of Feynman..."And perturbative descriptions on terms of Feynman rules are no good as long as the expansion can be shown to converge (which is probably wrong)."<BR/><BR/>Is this right? So Feynmann graph expansion fits with the axioms as long as the expansion diverges??Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8883034.post-1130167830134160762005-10-24T17:30:00.000+02:002005-10-24T17:30:00.000+02:00"In the discussion he had to admit that although h..."In the discussion he had to admit that although he has supergroups, the Hamiltonian is not an element of these"<BR/><BR/><BR/>That's a language issue which I have tried to discuss several times in the past, not with M. Zirnbauer himself, but with other members of that SFB on "Universality" which he is the head of. Following certain textbooks on "susy methods in statistical mechanics" some people in non-hep fields tend to use the word 'supersymmetry' whenever they encounter any graded vector space.<BR/><BR/>Mostly, all they do is to re-express matrix determinants as Berezin integrals over exponentials of bilinears in Grassmann variables. Hence their use of graded algebra is more like in Fadeev-Popov or BRST than in SUSY.<BR/><BR/>But there is a general confusion of terms. Because even when you are not dealing with susy proper, you may still work with honest supermanifolds.Anonymousnoreply@blogger.com