Solving Virasoro Constraints in Matrix Models

Abstract

This is a brief review of recent progress in constructing solutions to the matrix model Virasoro equations. These equations are parameterized by a degree n polynomial W_n(x), and the general solution is labeled by an arbitrary function of n-1 coefficients of the polynomial. We also discuss in this general framework a special class of (multi-cut) solutions recently studied in the context of \cal N=1 supersymmetric gauge theories.

9 pages, LaTeX, contribution to the 37th International Symposium Ahrenshoop on the Theory of Elementary Particles

References in corpus (17)

• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
• All genus correlation functions for the hermitian 1-matrix model
• A Large N Duality via a Geometric Transition
• Matrix Model Calculations beyond the Spherical Limit
• Higher genus correlators for the hermitian matrix model with multiple cuts
• Gravitational corrections in supersymmetric gauge theory and matrix models
• Breakdown of universality in multi-cut matrix models
• Partition Functions of Matrix Models as the First Special Functions of String Theory I. Finite Size Hermitean 1-Matrix Model
• Non-Perturbative Effects in Matrix Models and Vacua of Two Dimensional Gravity
• Unitary matrix integrals in the framework of Generalized Kontsevich Model. I. Brezin-Gross-Witten Model
• Matrix models vs. Seiberg-Witten/Whitham theories
• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• Complex Curve of the Two Matrix Model and its Tau-function
• On Equivalence of Topological and Quantum 2d Gravity
• DV and WDVV
• Unitary And Hermitian Matrices In An External Field II: The Kontsevich Model And Continuum Virasoro Constraints
• N=1 SUSY inspired Whitham prepotentials and WDVV

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