Two-matrix model and c=1 string theory

TL;DR

This paper demonstrates that the most general two-matrix model with bilinear coupling precisely captures the structure of $c=1$ string theory, including its constraints, correlation functions, and integrable hierarchy.

Contribution

It establishes an exact correspondence between the two-matrix model and $c=1$ string theory, revealing a unified underlying mathematical framework.

Findings

Two-matrix model with bilinear coupling underlies $c=1$ string theory.

$W_{1+ infty}$ constraints match exactly.

Correlation functions and integrable hierarchy correspond.

Abstract

We show that the most general two--matrix model with bilinear coupling underlies $c=1$ string theory. More precisely we prove that $W_{1+\infty}$ constraints, a subset of the correlation functions and the integrable hierarchy characterizing such two--matrix model, correspond exactly to the $W_{1+\infty}$ constraints, to the discrete tachyon correlation functions and to the integrable hierarchy of the $c=1$ string.