Matrix models as conformal field theories: genus expansion

Abstract

We obtain the topological expansion of the hermitian matrix model using its representation as a CFT on a hyperelliptic Riemann surface. To each branch point of the Riemann surface we associate an operator which represents a twist field dressed by the modes of the twisted boson. The partition function of the matrix model is computed as a correlation function of such dressed twist fields. The perturbative construction of the dressing operators yields a set of Feynman rules for evaluating the free energy and the loop observables at any genus.

17 pages, 4 figures

References in corpus (4)

• Instantons and Merons in Matrix Models
• Universal scaling limits of matrix models, and (p,q) Liouville gravity
• Non-Rational 2D Quantum Gravity II. Target Space CFT
• A Lagrangean formalism for Hermitean matrix models

Cited by in corpus (11)

• A & B model approaches to surface operators and Toda theories
• Matrix Models for Random Partitions
• Cut-and-Join operator representation for Kontsevich-Witten tau-function
• CFT and topological recursion
• Non-Perturbative Topological Strings And Conformal Blocks
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators
• An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
• Multi-boundary correlators in JT gravity
• A proof of loop equations in 2d topological gravity
• Cap amplitudes in random matrix models