Matrix Models, Quantum Penner Action and Two-Dimensional String Theory

TL;DR

This paper introduces a simple matrix model that, through the quantum Penner action, captures the all-order perturbative tachyon amplitudes in two-dimensional string theory at the self-dual radius.

Contribution

It establishes a connection between a basic hermitian matrix model and two-dimensional string theory via the quantum Penner action.

Findings

Correlation functions match all-orders perturbative tachyon amplitudes.

The model provides a new perspective on 2D string theory.

The quantum Penner action encodes rich structural information.

Abstract

A very elementary model of a single positive hermitian random matrix coupled to an external matrix is defined and studied. Expanding the exact effective action around its classical solution leads to the ``quantum Penner action'', from which a rich structure of correlation functions is obtained. These are shown to be equal to the all-orders perturbative expansion of tachyon amplitudes in the two-dimensional string at self-dual radius.