Worldsheet Duals to One-Matrix Models

TL;DR

This paper constructs a precise worldsheet dual to Hermitian one-matrix models, demonstrating exact agreement of correlators and providing a new toy model for gauge/string duality beyond the double-scaling limit.

Contribution

It introduces a concrete worldsheet theory dual to Hermitian one-matrix models, establishing a detailed gauge/string correspondence in the standard 't Hooft regime.

Findings

Matrix and string correlators agree to all orders in genus and coupling.

Explicit mapping between matrix traces and worldsheet vertex operators.

Correlators are expressed as integrals over Riemann surface moduli space.

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.