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Worldsheet Duals to One-Matrix Models

Alessandro Giacchetto, Rajesh Gopakumar, Edward A. Mazenc

Abstract

We derive a concrete closed string dual to any interacting Hermitian one-matrix model, away from the double-scaling limit. Matrix and string correlators manifestly agree, to all orders in the genus expansion and all orders in the 't Hooft coupling(s). The worldsheet theory consists of a supersymmetric B-twisted Landau-Ginzburg model coupled to 2d topological gravity. We provide a precise dictionary between traces of the matrix and vertex operators on the worldsheet. Matrix model correlators are explicitly mapped to computable integrals over the moduli space of Riemann surfaces. We perform several direct cross-checks on both sides of the duality. This work furnishes a detailed instantiation of gauge/string duality, in the standard 't Hooft regime, and hopefully a useful worldsheet toy model for the AdS/CFT correspondence, away from the free field limit.

Worldsheet Duals to One-Matrix Models

Abstract

We derive a concrete closed string dual to any interacting Hermitian one-matrix model, away from the double-scaling limit. Matrix and string correlators manifestly agree, to all orders in the genus expansion and all orders in the 't Hooft coupling(s). The worldsheet theory consists of a supersymmetric B-twisted Landau-Ginzburg model coupled to 2d topological gravity. We provide a precise dictionary between traces of the matrix and vertex operators on the worldsheet. Matrix model correlators are explicitly mapped to computable integrals over the moduli space of Riemann surfaces. We perform several direct cross-checks on both sides of the duality. This work furnishes a detailed instantiation of gauge/string duality, in the standard 't Hooft regime, and hopefully a useful worldsheet toy model for the AdS/CFT correspondence, away from the free field limit.

Paper Structure

This paper contains 8 sections, 32 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Main Result
  3. The Matrix Integrals
  4. The Dual String Theories
  5. The Correspondence
  6. Explicit Cross-Checks
  7. Relation to Double-Scaled Models
  8. Supplementary Material

Figures (1)

  • Figure 1: A pictorial representation of the worldsheet Feynman calculus computing semisimple CohFT correlators.