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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.
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326:, 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.
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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.
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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).
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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
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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
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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
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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
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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
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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
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Two observations, RedTomato: 1) Your proposal would require not just someone who knows a lot about supergravity, preferably a scientist, but also that person would have to be able to put as many of the incomprehensible scientific terms and jargon into lay language. Not many scientists can write
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The content of this section, and others for that matter, is completely obsolete. Plus, it has some mathematical imprecise statements. I will write soon enough a complete and modern formulation of four-dimensional
Supergravity and its mathematical structure. In fact, I think this section should be
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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
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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
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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
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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
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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
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As opposed to what? Does the MSSM predict a non-local symmetry, a global symmetry, no symmetry? Is local supersymmetry a unique prediction? Why is it important? Did I mention that I can't stand most parenthetical statements? If it's worth saying, say it! If it's a distraction, don't bother
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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
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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
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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.
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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
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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.
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As opposed to global supersymmetry. One could get technical and mention that any theory that incorporates local supersymmetry necessarily incorporates gravity. A related statement that for any supersymmetric theory that includes gravity, the supersymmetry must be realized locally.
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They are right. Why don't you physicists make a "Supergravity for dummies" - after all, guys like
Hawking keep simplifying the terminology rather well, so maybe that's a way? This is an encyclopedia, it wants to EXPLAIN the topic to people WHO DO NOT KNOW THE DETAILS already!
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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
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is written in the tone of a lecture, with frequent use of "We have" and "We will", etc. This is in contrast to the rest of the article, and seems non-encyclopedic to me, and needs to be updated to remove the usage of the first-person pronoun ("we").
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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
Knowledge will have experts, and they'll read my articles and laugh (or just erase them).
695:(Watson's Unified Strings Theory)...(D: dimension, s: space, t: time, st: spacetime, rs: regular space, hs: hyperspace, a: aspects, rt: regular time, ht: hypertime). Note: 'hyperspace' is often referred to as "higher dimensions". - Ben Franklin
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about their own disciplines in terms lay people would understand, and 2) This article isn't really that long. A lot more could be written about supergravity. This article itself, so far, is pretty much just an introduction to the subject. –
318:: 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
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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?
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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.
351:. 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
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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)
540:"Together, these imply that, in supergravity, the supersymmetry is a local symmetry (in contrast to non-gravitational supersymmetric theories, such as the Minimal Supersymmetric Standard Model (MSSM))."
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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.
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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.
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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)!!
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percentage won't be physicicsts, but want to grok as much as possible, just for the thrill. Try to serve all three audiences well.
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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
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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.
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As mentioned above - this page suffers from being incomprehensible to a large part of the audience
Knowledge is aimed at.
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Why is there so much detail on higher dimensional SUGRA (in 11, 10, and 9 dimensions) and none at all on 4D SUGRA?
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Supergravity theories are often said to be the only consistent theories of interacting massless spin 3/2 fields.{{
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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)?)
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Recommend it stay out of the article until a verifiable source can be found and included with it. –
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maximal compact subgroup. Spin(2) is its universal cover, SU(2), which is not a subgroup of SO(3).
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He's really right. I don't even know what supergravity IS. Please fix this article, I want to know.
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on Knowledge. If you would like to participate, please visit the project page, where you can join
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The following is moved here because it is a claim that has gone uncited for a very long time:
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This article is confusing. It uses terms that are unfamiliar to the average person.
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Guys, please take a moment to follow several conventions used in WP talk pages.
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The section or sections that need attention may be noted in a message below.
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This is a good question, it was way before my time (I just trusted
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or the squashed 7-sphere, with symmetry group SO(5) times SU(2).
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This topic is in need of attention from an expert on the subject
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4D_N_=_1_SUGRA section written as a first-person lecture
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Sign your comments by using four tildes, like so: ~~~~
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Knowledge level-5 vital articles in Physical sciences
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Please make the corrections, then. Several remarks:
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301:D=11 Supergravity with Local SU(8) Invariance
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