Topological Matrix Models, Liouville Matrix Model and c=1 String Theory

Abstract

This is a review of some beautiful matrix models related to the moduli space of Riemann surfaces as well as to noncritical c=1 string theory at self-dual radius. These include the Penner model and the W-infinity model, which have different origins but are equivalent to each other. In the final section, which is new material, it is shown that these models are also equivalent to a Liouville matrix model. We speculate that this might be interpreted in terms of N D-instantons of the c=1 string.

latex, 35 pages, based on lectures delivered at the IPM Workshop on String Theory, Bandar-e-Anzali, Iran, in October 2003, v5: few corrections

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Cited by in corpus (17)

• Liouville Field Theory -- A decade after the revolution
• A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model
• From Free Fields to $AdS$ -- III
• Modular Bootstrap for Boundary N=2 Liouville Theory
• Flux Backgrounds in 2D String Theory
• On a worldsheet dual of the Gaussian matrix model
• Matrix Models, Integrable Structures, and T-duality of Type 0 String Theory
• c=1 Matrix Models: Equivalences and Open-Closed String Duality
• On an Airy matrix model with a logarithmic potential
• Liouville D-branes in Two-Dimensional Strings and Open String Field Theory
• Topological B-model and $\hat{c}=1$ String Theory
• New critical behavior in a supersymmetric double-well matrix model
• Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$
• The Kontsevich Connection on the Moduli Space of FZZT Liouville Branes
• Supersymmetric double-well matrix model as two-dimensional type IIA superstring on RR background
• c=1 from c<1: Bulk and boundary correlators
• A Matrix Model with BMS${}_3$ Constraints