The partition function of 2d string theory

TL;DR

This paper derives a compact expression for the generating functional of tachyon correlators in 2D string theory, revealing connections to integrable systems and providing a Kontsevich-Penner integral representation.

Contribution

It introduces a new explicit formula for the generating functional in 2D string theory, linking it to KP flow and $W_{1+ ablafty}$ constraints, and presents a Kontsevich-Penner integral form.

Findings

Explicit generating functional for tachyon correlators derived

Connections established between 2D string theory and integrable systems

Kontsevich-Penner integral representation obtained

Abstract

We derive a compact and explicit expression for the generating functional of all correlation functions of tachyon operators in 2D string theory. This expression makes manifest relations of the $c=1$ system to KP flow and $W_{1+\infty}$ constraints. Moreover we derive a Kontsevich-Penner integral representation of this generating functional.