Erik Verlinde recently gave another talk on emergent gravity. This talk has a little more substance than the May one, but unfortunately it is targeted at the stringy audience, and this causes Verlinde to appear very vague and unsure of himself.

There were a few notable moments. At one point an audience member, probably Polchinski, made a remark that Verlinde was secretly talking about a Fermi surface in twistor space, and Verlinde later agreed with this somehow. He also discusses Berry phases in connection to eigenvalues for Hermitian matrices, in the context of what he calls his new pre-geometric matrix theory, although there was no attempt to actually outline a theory. Verlinde was treated with respect.

7 years ago

'In his after-dinner remarks at a Strings conference at (K)ITP Santa Barbara in the mid-1990’s, Joe Polchinski proposed a “Fermi liquid on twistor space” as a half-joking

ReplyDeleteanswer to the question of “what is string theory?”.' (see footnote, page 24) The expression also shows up in a footnote on page 20 here.

Link from Verlinde on Wikipedia

ReplyDeletehttp://supernova.lbl.gov/~evlinder/turner.pdf

Michael Turner, publ. year unknown.

Black Hole Berry Phase

ReplyDeletehttp://arxiv.org/abs/0809.5062

Karabali and Nair have been studying higher dimensional QHE for some time and have already given a matrix model description for LLL (lowest Landau level) dynamics. See "Quantum Hall Effect, Bosonization and Chiral Actions in Higher Dimensions" (arXiv:1005.4341[hep-th]), from earlier this May.

ReplyDeleteYeah OK, so I don't find this idea that interesting. They use mainly classical techniques.

ReplyDeleteThey basically cover the CP^k cases with unitary symmetry in the LLL. Of course Zhang and Hu (4D QHE) also explored an 8D QHE using the octonions and the Hopf fibration S^15 -> S^8 (cond-mat/0306045). Note this is precisely the same Hopf fibration used by Polchinski to describe the S-dual of the open heterotic string, as a type I D1-brane ending on a type I D9-brane (hep-th/0510033). It is noted by Polchinski that the construction can likely be embedded in heterotic matrix theory.

ReplyDeleteVerlinde might find such constructions useful.

Ah, yes I can see that Verlinde should probably head this way, since he is unlikely to suddenly find a love for category theory and abstract matrix algebras.

ReplyDeleteI wonder what happens to open strings when the Universe expands. They must also expand? Or do they divide like gluons? Is that the Hopf nets?

ReplyDeleteGravitons should then be closed strings with no need to divide = gravity is decreasing all the time? After Big Bang was a high gravity.

But matter is increasing?

Ulla, that's an excellent basic question. I want to give you a direct answer rather than just a link, but I may need to think about it for a few days, so please look here again.

ReplyDeleteAny curvature of space - any deviation from "flatness" (Minkowski space) - should be "made of gravitons", so the expansion of the universe must have a description in terms of closed strings interacting with each other. But I need to think about what that description is.

Update: It may take me weeks to provide an authoritative answer. The simplest string models of an expanding universe describe how strings move against that background, but they don't explain the background itself. There may be a better explanation e.g. in string field theory.

ReplyDeleteI guess this is the problem with the emergent space Verlinde talked of.

ReplyDeleteThanks anyway.