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Question 1: What is the status of string random matrix models (~ triangulated random surfaces) with c>1?

In my limited search, I have just come across a few papers by Frank Ferrari (in 2000-2002) on this. But, they applied, if I understand correctly, to a few cases with some specific kind of singularities in their moduli space or some higgs field. See his lecture at http://arxiv.org/abs/hep-th/0205171 and references therein.


On a slightly different note...
Question 2: How is the BFSS matrix model (and its derivatives, like the ones mentioned at Good introductory text for matrix string theory) related to the random matrix models of triangulated worldsheets? My understanding is that the former is a nonperturbative formulation of some critical string theories, while the latter is a perturbative formulation of (noncritical only?) string theories. But, what are the similarities and connections between these two applications of random matrix theories?

PS: some references (especially some pedagogical ones) would also be of immense help!

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I don't know the answer to question 1, but for question 2, the close relative of the matrix models are the 2-brane approximations of deWit, Hoppe, and Nicolai, who essentially give the same 1d matrix models as an approximate description of 11-dimensional supergravity 2branes many years before BFSS. The BFSS work discovers the a physical interpretation of this kind of description, in the D0 branes, but mathematically, the two models look the same.

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  • $\begingroup$ Thanks for addressing question 2. But what is the relation between deWit, Hoppe & Nicolai matrix model (as used in BFSS etc) and Wigner random matrix model (as used in string worldsheet triangulation etc)? $\endgroup$ – GuSuku Sep 29 '11 at 4:27
  • $\begingroup$ Beats me! I never studied these. I'll look into it, and try to see. $\endgroup$ – Ron Maimon Sep 29 '11 at 4:39

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