Status of String Random Matrix Models w/ c>1

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SUMMARY

The discussion centers on the status of string random matrix models with central charge c>1, specifically referencing Frank Ferrari's work from 2000-2002 that addresses singularities in moduli space and Higgs fields. Additionally, the relationship between the BFSS matrix model and random matrix models of triangulated worldsheets is explored, highlighting the former as a nonperturbative formulation of critical string theories and the latter as a perturbative approach to noncritical string theories. The inquiry seeks to clarify the connections and similarities between these two frameworks within random matrix theory.

PREREQUISITES
  • Understanding of string theory concepts, particularly critical and noncritical string theories.
  • Familiarity with random matrix theory and its applications in theoretical physics.
  • Knowledge of moduli space and its significance in string theory.
  • Basic comprehension of nonperturbative and perturbative formulations in quantum field theory.
NEXT STEPS
  • Research Frank Ferrari's papers on string random matrix models, particularly those from 2000-2002.
  • Explore the BFSS matrix model and its implications for critical string theories.
  • Investigate the role of triangulated worldsheets in random matrix models.
  • Study the connections between perturbative and nonperturbative approaches in string theory.
USEFUL FOR

The discussion is beneficial for theoretical physicists, string theorists, and researchers interested in the intersection of random matrix theory and string theory, particularly those focusing on critical and noncritical models.

crackjack
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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.
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On a slightly different note...
Question 2: How is the BFSS matrix model (and its derivatives for other critical string theories) 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?
 
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