From: Aaron Bergman Subject: Re: This Week's Finds in Mathematical Physics (Week 154) Date: 14 Aug 2000 17:36:48 GMT Newsgroups: sci.physics.research,sci.physics,sci.math Summary: [missing] In article <8n4pd7$qaf$1@mortar.ucr.edu>, baez@math.ucr.edu (John Baez) wrote: Rearranging the order a little bit. > 3) Juan Maldacena, The large N limit of superconformal field theories > and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231-252, preprint > available as hep-th/9711200. > > 6) Edward Witten, Anti-DeSitter space and holography, Adv. Theor. > Math. Phys. 2 (1998) 253-291, preprint available as hep-th/9802150. > > 7) S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory > correlators from noncritical string theory, Phys. Lett. B428 (1998) > 105-114, preprint available as hep-th/9802109.> > AdS/CFT is old news by now (which isn't to say that there's still not a whole lot of interesting stuff going on with it.) A huge review article on this is hep-th/9905111. [..] > > 5) Edward Witten, String theory dynamics in various dimensions, > Nucl. Phys. B443 (1995) 85-126, preprint available as hep-th/9503124. > > This paper was also important in the quest to understand dualities: > among other things, it argued that the type IIA superstring in 10 > dimensions has as a low energy limit 11-dimensional supergravity - > reduced to 10 dimensions by curling up one dimension into a very > *large* circle. I'm not sure what you're saying here. In this paper, Witten argues that the strong coupling limit of type IIA string theory is something that has, as its low energy limit, 11D supergravity. The size of the 11th dimension is related to the string coupling constant (equivalently, the dilaton). > > 8) Joseph Polchinski, Dirichlet branes and Ramond-Ramond charges, > Phys. Rev. Lett. 75 (1995) 4724-4727, preprint available as > hep-th/9510017. > > 12) Edward Witten, Bound states of strings and p-branes, Nucl. Phys. > B460 (1996), 335-350, preprint available as hep-th/9510135. Clifford Johnson has a huge review on what's been done with D-branes since then in hep-th/0007170. [...] > 11) C. M. Hull and P. K. Townsend, Unity of superstring dualities, > Nucl. Phys. B438 (1995) 109-137, preprint available as hep-th/9410167. > > More about dualities, obviously! (But also some stuff about the > exceptional Lie group E7, which is bound to tickle the fancy of any > exceptionologist.) Actually, the appearance of the E series of Lie groups here is a consequence of a discovery of Cremmer and Julia in the late seventies that the entire E series shows up with you compactify 11D supergravity on tori. On the huge review front, for U-duality, there's hep-th/9809039. Anyways, string theory being the absurdly fast-moving field that it is, all the current rage is noncommutative geometry. This started with a paper by Connes, Douglas and Schwarz hep-th/9711162. Then Seiberg and Witten did their thing hep-th/9908142. This has led to all sorts of neat stuff like finding D-branes as solitons, string theories without gravity (NCOS), open membrane theories and other stuff. There's also been a conjecture due to Sen that the open string tachyon in bosonic string theory actually corresponds to an instability of a D25 brane. This has been somewhat verified by numerical calculations in open string field theory. Sen's conjecutre also is related to the tachyon that occurs in the open strings that connects a D-brane and an anti-D-brane. Sen showed that you can construct whorl-like solutions for this tachyon that carry the charge of lower level D-branes. The conjecture is that when the D-branes annihilate, you are left with a D-brane of smaller dimension. Then, in some sense, if you fill spacetime with a bunch of D9/\bar{D9} pairs, everything is hiding in the vector bundle structure that lives on these. This means that branes are classified by K-theory, a fact which was actually postulated a bit before this construction became clear. Now, Witten has all sorts of ideas (hep-th/0007175) and I've checked Wegge-Olson out of the library (and I'm borrowing Brylinksi from a friend). Aaron -- Aaron Bergman ============================================================================== From: shocklee@Princeton.EDU (Paul D. Shocklee) Subject: Re: This Week's Finds in Mathematical Physics (Week 154) Date: 14 Aug 2000 17:37:19 GMT Newsgroups: sci.physics.research,sci.physics,sci.math John Baez (baez@math.ucr.edu) wrote: > Another important book, especially for people who like exceptional groups, > is this one - I've referred to it before, but I just finally took a good > look at it: > 18) F. Reese Harvey, Spinors and Calibrations, Academic Press, 1990. > There's some incredible stuff here about 7-dimensional Riemannian > manifolds whose holonomy groups lie in the exceptional Lie group G2. > I bet this stuff is gonna be important in string theory someday - if it > isn't already. After all, G2 is the automorphism group of the octonions, > and it has a 7-dimensional irreducible representation on the imaginary > octonions; as explained in "week104" by Robert Helling, the octonions > are secretly what let you write down the superstring Lagrangian in 10d > spacetime. They are important! If you want to directly compactify 11-dimensional supergravity/M-theory to a theory with N=1 supersymmetry in 4 dimensions, which is what people like for phenomenological reasons, you need a 7-dimensional manifold of G2 holonomy (just as you need manifolds of SU(3) holonomy, i.e. Calabi-Yau manifolds, in six dimensions). I have seen these referred to as "Joyce manifolds," after Dominic Joyce, who constructed several examples of such spaces. (I didn't know there was so much known about them. I'll have to check out the above book; I see that our library in Iceland has a copy.) Unfortunately, these models are afflicted by the usual problem of 11-d SUGRA compactifications, which is that they are non-chiral, so these days people seem to be concentrating more on Horava-Witten compactifications, with M-theory on S^1/Z_2 times a Calabi-Yau, or on an orbifold. If you're interested, you might want to check out Papadopoulos and Townsend, "Compactification of D=11 supergravity on spaces of exceptional holonomy," http://xxx.lanl.gov/abs/hep-th/9506150 -- Paul Shocklee Graduate Student, Department of Physics, Princeton University Researcher, Science Institute, Dunhaga 3, 107 Reykjavík, Iceland Phone: +354-525-4429