Talk:Supergravity

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The 10d models, that is massless IIA string theory and also IIB when there's a circle around, are equivalent to compactifications of the 11d circle. Thus there can be no experimental evidence for the 10d theory over the 11d theory, and its no harder to find models in the 11d theory than in its 10d description. While in general the 11d theory isn't defined, in these cases it is defined via the duality. Thus I disagree with the entirety of the section on the failings of the 11d theory (while the 11d theory has no shortage of failings, they are not remedied in the 10d formulation). In addition, the first, second and fourth points in the section are incorrect: (1) There are no compactifications of M-theory that produce the standard model, so the point is vacuous. However there are plenty of supersymmetric compactifications. The compactification to which the author refers has 32 supercharges, much more than phenomonologists have ever asked of us. (2) It is not difficult to create chiral fermions in 11d compactifications, although such compactifications do require singularities in the compactification manifold. (4) Gauge theory realizations in M-theory are not always anomalous. The discussion also contains three false points. (1) 11 dimensions are not necessary to get the standard model gauge group, nor has Witten made such a proposal, although 11d may be necessary to get some features that Witten finds attractive. (2) The content of the CJS 11d supergravity is not the unique content that gives an equal number of bosons and fermions, but it is, classically (that is, up to changes that vanish when the equations of motion are imposed) the only known supersymmetric 11d action (I probably also need to impose that no fields have spin higher than two). (3) The two 11d compactifications mentioned may be the only ones that preserve all 32 supercharges (maybe some planewave compactification also does?), but is not the only one that leaves an equal number of fermions and bosons. There are plenty of other compactifications that leave some supersymmetry.

Sorry for the long comment, but anyway, I think it'd be good to have a rewrite for the first two sections. The opening is good. JarahE 19:13, 13 March 2006 (UTC)

Please make the corrections, then. Several remarks:

• I wrote most of the article as it currently stands. I sort of understood some of this stuff 20 years ago, but even then my understanding was shaky, and it is now clouded by bad memory. I was trying to capture what it was about supergravity that made it so exciting in the mid-80's; this was before M-theory, and at the dawn of wider acceptance of string theory, so the perceptions about how the standard model may or may not fit was of that era. if you can fix the content without removing why it was that everyone thought this was such an exciting thing back then, that would be great.
• As to the target audience: try to keep the writing style as if this was the a physics colloquim: a small percentage of readers will have a background in string theory, a large percentage will have some but not much background in field theory and/or gravition, possibly not both, and some smaller percentage won't be physicicsts, but want to grok as much as possible, just for the thrill. Try to serve all three audiences well. linas 01:32, 14 March 2006 (UTC)

Ok, don't worry about it. I didn't want to be hostile, I just want to be able to erase most of the article without being branded a vandal. When I have some time I can try to make a rewrite that conforms to your above criteria. The article will still be a bit incomplete though as SUGRAs in less than 10d are also interesting and I don't know enough about them to feel comfortable writing anything, nor do I know all that much about the others. Some day Wikipedia will have experts, and they'll read my articles and laugh (or just erase them). JarahE 16:26, 14 March 2006 (UTC)

I reviewed your edits, and they're fine, they're fully within the spirit of WP. The whole point of open editing is in order to have everyone fix everyone-elses mistakes. No one will ever mistake you for a vandal. Only one comment: remember that this is an encyclopedia, not a pop-lit magazine. Don't get too informal, too hip. The text itself is great, and its ok to write fun-to-read sentances. The section titles "fist we stared in 4 ..." I found to be a little too informal. 00:43, 15 March 2006 (UTC)

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or the squashed 7-sphere, with symmetry group SO(5) times SU(2).

But this group doesn't contain SU(3)_C, or am I missing something here? Or for that matter, Spin(8) doesn't contain SU(3)_C× SU(2)_W. QFT 20:23, 26 March 2006 (UTC)

This is a good question, it was way before my time (I just trusted Linas on the history and redid the physics). Freund-Rubin don't seem to have actually calculated the gauge group in their paper. I remember that in the De Wit-Nicolai series of papers in the mid 1980s on FR's AdS^4xS^7 compactification they say that (maybe thanks to the fermions, since somehow it comes from a contraction of the vielbien with gamma matrices) somehow the SO(8) gauge symmetry coming the S^7 gets enhanced to an SU(8) gauge symmetry. This SU(8) gauge symmetry I guess must be the same one that you quotient by when you say that the moduli space for a T^7 compactification of 11d SUGRA is E_7/SU(8). So somehow maybe the idea was that the S^7 is just the bosonic part of a supermanifold, and the full symmetry of the supermanifold is SU(8).

Really De Wit and Nicolai go even further in D=11 Supergravity with Local SU(8) Invariance and they say that the SU(8) symmetry was already there before you compactified, which they somehow find by contracting a 7x7 block of the vielbien with the gamma matrices. In a later paper they try an 8x8 block and they find that the SU(8) lives in an SO(16) gauge symmetry. Now adays they're more ambitious and take 10x10 blocks or even the whole 11x11 elfbein and make infinite-dimensional subalgebras of hyperbolic Kac-Moody algebras. But really the SU(8) was big enough already to fit the standard model. JarahE 21:21, 26 March 2006 (UTC)

To QFT: Thank you for your improvements to this page. However, I stand by my phrase about all irreducible spinors in a given dimension having the same dimensionality. Maybe the confusion is that I should have highlighted the word irreducible. For example, clearly the Dirac and Weyl reps have different dimensionalities, but in odd dimensions there is no Weyl rep and in even dims the Dirac rep is reducible, thus there is no case in which both are irreps and so no contradiction. Similarly, Majorana and Dirac reps are of different dimensionalities, but when Majorana reps exist, Dirac reps are reducible so again only one is irreducible at a time and so there is no contradiction. There's a similar story with Weyl vs MW and Majorana vs MW. The only nontrivial case is when Weyl and Majorana exist but not MW (like in our 3+1 dimensions). Here they're both irreducible, but they both have the same dimension. Thus the dimensionality of the irreps is the same in every case, and the number N is well-defined. Anyway, so I'd be for putting back the sentence that you'd erased.

I agree that your comment about AdS in the Freund-Rubin section was good though. However also the spin <3/2 thing that you just added seems gratuitous. While often we use this kind of 4d language for spinors in arbitrary dimensions, it's a bit ill-defined (really you need to classify them by Young tableaux, not half-integers, above 3+1 dims). The spin 3/2 rep is just a tensor product of the vector and spin 1/2, so the classification of spin 1/2 spinors is the same as that of spin 3/2 spinors. Of course, maybe you're right that something to this effect should be in the text. JarahE 21:47, 26 March 2006 (UTC)

More for QFT: I didn't understand the word real you put before representations. Representations are counted by natural numbers, so I don't think there's any confusion that they can be double-counted by not specifying real. But more importantly, people say that the Majorana rep is a real spinor rep, so I think this extra word will give people the false impression that we're counting Majorana reps. Really you count whichever rep is irreducible.

About your deletion of my comments on the projective representation, it appears as though there's some maximal space for comments and so I could only read the beginning of what you wrote. And so, needless to say, I don't see what your objection is. In the part that I read, you appeared to be saying that the overall phase on a field is somehow physical, in contrast to particle wavefunctions. If this is indeed what you were saying, I disagree. I'd guess that by field you just meant the second quantized wavefunction. To talk about the spectrum it suffices to work in first quantization, but really the only difference here is whether you quantize the position and momentum or the Fourier modes of the field ... ie, in both first and second quantization an overall phase on a field or equivalently on a vector in the Hilbert space (as these are modules of the fields) does not change the physical state. Physical states correspond to rays in the Hilbert space.

Are you objecting to my claim that the Hilbert space vector corresponding to a fermion doesn't transform under any rep of the Lorentz group? A rotation by 360 degrees is the identity element of the Lorentz group, thus in any representation it is the identity (because representations are homomorphisms, and homomorphisms take the identity to the identity) ... but it isn't the identity on a fermion field, it is multiplication by -1, thus its not a rep. It is, however, a projective rep.JarahE 22:04, 26 March 2006 (UTC)

Hello again. This last comment that you added on not being able to get the other two symmetry groups from string theory is interesting and I haven't seen it before. What goes wrong if you try to embed these in string theory? ie ... if you try for example to put a U(1)^496 current algebra on one side of a heterotic string? I guess you must be right, since the O9 plane has a tension of -16 and so you can't have a gauge group with rank not equal to 16 without some tadpole cancellation problems ... is that it?JarahE 22:12, 26 March 2006 (UTC)

Dear 128.175.189.45. Thank you for your recent additions to the supergravity page. I agree with nearly everything, except for your claim that Spin(N) is a subgroup of the Lorentz group. For example, consider massive particles in 3+1 dimensions, so the little group is SO(3), which is also its own maximal compact subgroup. Spin(2) is its universal cover, SU(2), which is not a subgroup of SO(3).

Spin(2) is a Z₂ central extension of SO(3), which is what we want because, as I wrote in the text erased by QFT, symmetries (in this case SO(3)) of the states act on Hilbert space vectors in projective representations, and the projective representations of SO(3) are isomorphic to the ordinary representations of Spin(2)=SU(2). Do you agree? (ie, do you agree that Spin(2)=SU(2) and that SU(2) is not a subgroup of SO(3)?)JarahE 14:03, 27 March

Guys, please take a moment to follow several conventions used in WP talk pages.

• Indent your responses, by using a colon in front.
• Sign your comments by using four tildes, like so: ~~~~
• Occasionally start new subject headings.

Right now, its hard to see who said what, and, in the last few comments, you all seem to be in violent agreement about (something as trivial as) SU(2)!! linas 04:36, 11 June 2006 (UTC)

[edit] History of physics

As this article has gotten long, it may be advisable to split the history part out into its own section, and put it under the cat Category:History of physics. linas 04:28, 11 June 2006 (UTC)

Agreed. Really my hope is that, since Supergravity is such a big field, the article would eventually get split up into a category with each section as an article, in particular each SUGRA theory I think will eventually deserve it's own article. Obviously this is a long way off, even the definitions of the various SUGRA theories have still yet to be included, and they are still each too small to become their own articles. But I agree that the history section is already big enough to be split off. But then since this article still has the all-encompassing title supergravity, I guess it should still have a few sentences about history, although I don't think that I'd be a good person to write them.--JarahE 07:17, 2 July 2006 (UTC)