Integrable flows in c=1 string theory

TL;DR

This paper reviews a method to construct integrable deformations of c=1 string theory using matrix models, focusing on flows generated by momentum or winding modes that satisfy the Toda hierarchy.

Contribution

It introduces a systematic approach to deform c=1 string theory via primary fields within a matrix model framework, highlighting integrability properties.

Findings

Flows generated by momentum or winding modes are integrable.

These flows satisfy the Toda lattice hierarchy.

The method applies to deformations using primary fields.

Abstract

In these notes we review the method to construct integrable deformations of the compactified c=1 bosonic string theory by primary fields (momentum or winding modes), developed recently in collaboration with S. Alexandrov and V. Kazakov. The method is based on the formulation of the string theory as a matrix model. The flows generated by either momentum or winding modes (but not both) are integrable and satisfy the Toda lattice hierarchy.