From Matrices to Strings and Back

TL;DR

This paper constructs a string dual for the Gaussian matrix model using Strebel differentials, proposing a worldsheet theory that localizes on specific Riemann surface points and relates to matrix model Feynman diagrams.

Contribution

It provides an explicit construction of a string dual for the Gaussian matrix model and introduces a worldsheet theory based on Strebel differentials with localized correlators.

Findings

String dual constructed for Gaussian matrix model

Worldsheet theory localizes on finite Riemann surface points

Correlators expressed as sums over Feynman diagrams

Abstract

We discuss an explicit construction of a string dual for the Gaussian matrix model. Starting from the matrix model and employing Strebel differential techniques we deduce hints about the structure of the dual string. Next, following these hints a worldheet theory is constructed. The correlators in this string theory are assumed to localize on a finite set of points in the moduli space of Riemann surfaces. To each such point one associates a Feynman diagram contributing to the correlator in the dual matrix model, and thus recasts the worldsheet expression as a sum over Feynman diagrams.