tag:blogger.com,1999:blog-8666091.post4665056397688679531..comments2020-03-13T03:28:45.250+01:00Comments on The Reference Frame: Tevatron falsifies Connes' model of physicsLuboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-8666091.post-20083851382278091622008-08-27T22:31:00.000+02:002008-08-27T22:31:00.000+02:00Well it happened to be not so secret at all; it is...Well it happened to be not so secret at all; it is reprinted in a old Appelquist-Chodos-Freund volume on Kaluza Klein theories which a friend happened to have nearby.<BR/><BR/>The problem is deeper than having chiral fermions: once you have zeroed in 2+4k, "the question is whether V-A gravity can reduce to V-A weak interactions in 4 dimensions"<BR/><BR/>It seems that the pivotal point, at that time, was a non-go theorem from Atiyah-Hirzebruch: "that for any continuous symmetry group, abelian or non abelian, the Dirac zero modes form a real representation". Witten was able to expand this theorem to cover the Rarita-Shwinger operator, partly. Then sect V of the paper nails the coffin for Kaluza Klein and section VI opens the chest of elementary, no KK, gauge fields in the 4+n dimensional space... and the topological justification of family multiplicity: "The Dirac operator becomes the d and d* operator on differential forms, and the number of zero modes (weighted by chirality) is the Euler characteristic".<BR/><BR/>Really an explanation from Castellani et al. book, in addition to your argument, in addition to my own generally known credulity, are enough to acknowledge what is happening. But I was interested on some perspective too. With that paper, Witten is told to have fulfilled the other role of a lamplighter: definitively lighting off the Kaluza Klein lamp. It proves that a SM-like gauge group can not appear from the isometries of a compact space.<BR/><BR/>It seems that the 2 mod 8 argument was first exposed by Wetterich in NucPhysB 222, p 20 (1983).<BR/><BR/>Now, what amazes me is that there seems to have no problem in the limit of infinite mass of W and Z, where the standard model becomes again vector-like, and where nine dimensions are enough to have a group SU(3)xU(1) as isometries of some 5 dimensional manifold. One could have taken some time trying to grow from this nonproblematic nine dimensional theory to some 10 or 11 dimensional one.Alejandro Riverohttps://www.blogger.com/profile/16181521111080562335noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-23258432344781539142008-08-27T16:35:00.000+02:002008-08-27T16:35:00.000+02:00I don't have any scanned copy but I am also sure t...I don't have any scanned copy but I am also sure that it is ludicrous to ask for a secret 1985 talk at some island because what you want to be explained is elementary material explained in almost every textbook of string theory and every textbook of representation theory of Lie groups.<BR/><BR/>There is absolutely no problem to get a chiral theory by compactifying a 10+8k dimensional theory to 4D: it's exactly the right dimension where a chiral 4D theory is possible. Because in 10+8k Lorentzian dimension, one has Weyl Majorana (chiral real) spinors, 16, and they get decomposed to (2,4)+(2bar,4bar) under SO(3,1) x SO(6), which links the 4D chirality (2 vs 2bar) to the 6D chirality (4 vs 4bar). <BR/><BR/>Note that it is essential for the compact manifold to be even-dimensional, otherwise there is no chirality there, and it must be 2+8k or 6+8k to get complex reps that can be linked to the complex reps of SL(2,C) = SO(3,1) (locally): the other even dimensions have real or pseudoreal spinors and couldn't lead to a chiral theory either. <BR/><BR/>The other possibility to consider is from 6+8k dimensions to 4D. There might exist some more elementary explanation why it's not possible, but surely 2 hidden dimensions are too simple, and only torus (full SUSY) preserves some SUSY. 6+8 = 14 dimensions is already too much, not admitting a physical supersymmetric theory. Even without SUSY, you could have problems.<BR/><BR/>Connes' dimensionality is exactly the same one as in string theory, mod 8.Luboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-29211680842440438842008-08-27T11:59:00.000+02:002008-08-27T11:59:00.000+02:00Lubos, I am looking for some scanned copy of Witte...Lubos, I am looking for some scanned copy of Witten's talk in Shelter Island II. You know, the one which did the turn away from Kaluza Klein gauge groups and towards embracing other alternatives: SO(32), E8xE8 (and, lately, D-brane junctions). Do you happen to have a copy?<BR/><BR/>THis is most of a private request, but I am pasting exactly in this thread because in some sense Connes "truncation" is a bypass of that theorem. Note that Alain deduces independently the need of 2 mod 8 (claimed in that paper, according Castellani book) but then it gets a chiral theory. Note that a precondition for it to happen was a non null index for the Dirac operator.Alejandro Riverohttps://www.blogger.com/profile/16181521111080562335noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-25211212397750617962008-08-07T06:11:00.000+02:002008-08-07T06:11:00.000+02:00Dear physicist with an Arab name who tried to post...Dear physicist with an Arab name who tried to post here,<BR/><BR/>sorry, I couldn't approve your message because it would be introducing emotions that have absolutely no room in science, especially not in this very technical discipline.<BR/><BR/>With the current understanding, I don't think that there was anything "beautiful" about the theory, and even if it looked so, it would be completely irrelevant because science has different goals. Play the Feynman video to get a hint.<BR/><BR/>I am always jubilant in similar situations because whenever the truth about a question becomes crisp and transparent, I am jubilant. That's how I am. I prefer the naked truth over irrational brainwashing and over collective celebration of beautiful emperor's clothes that don't really exist.<BR/><BR/>It was Alain Connes who was recommended to learn string theory and I think it is an excellent idea. I didn't tell it to you, which would probably be a less good idea.<BR/><BR/>Incidentally, 1982 is 26 years ago. You surely don't expect sensible people to judge the value of a recently formulated theory by ad hominem episodes that are moreover separated from the present era by 26 years, do you?<BR/><BR/>All the best<BR/>LubosLuboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-63434455379109755742008-08-06T07:44:00.000+02:002008-08-06T07:44:00.000+02:00Dear Alejandro, I was asked the question about NCG...Dear Alejandro, I was asked the question about NCG as a truncation of string theory in the fast comments, look there.<BR/><BR/>I don't know what "lack of SUSY" you're talking about. I think it is not a settled question and the recent Tevatron data lead me to believe that SUSY at the LHC is more likely than 50%. I raised my guess to 60% and incidentally, I was surprised to see the exact same figure at a recent Cosmic Variance posting.<BR/><BR/>Most stringy dualities are clearly invisible to a truncation of the theory, so if you interpret NCG as the truncation of the string compactifications to the zero modes, NCG will have nothing to say about dualities, except for trivial comments. <BR/><BR/>For example, if the same NCG model would represent two descriptions that would be mirror-symmetric to one another, it would "have" mirror symmetry in it. But you can't really decompactify the finite-dimensional non-commutative manifolds so you can't map them to the normal Calabi-Yaus.<BR/><BR/>You probably overestimate what I meant by the comment. What I really meant was to invite Alain Connes to learn string theory properly - the NCG picture has some relevant tools but it is of course a very small fraction of what is needed to make realistic model-building including quantum gravity.Luboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-89399185293297318272008-08-06T00:43:00.000+02:002008-08-06T00:43:00.000+02:00If only to fix ideas... Why do you think that Conn...If only to fix ideas... Why do you think that Connes model is/could be a truncation of string theory? Do you have some conjecture to explain the lack of SUSY? Any idea about how the web of string dualities fits in the NCG scenario?Alejandro Riverohttps://www.blogger.com/profile/16181521111080562335noreply@blogger.com