On Connection between Topological Landau-Ginzburg Gravity and Integrable Systems

TL;DR

This paper explores the relationship between topological Landau-Ginzburg gravity and integrable systems, showing how gravitational flows relate to the KP hierarchy and tau-functions of the Generalized Kontsevich Model.

Contribution

It establishes a connection between gravitational descendants in topological Landau-Ginzburg theories and the dispersionless KP hierarchy, linking to the tau-function of the Generalized Kontsevich Model.

Findings

Flows change the target space to a punctured plane and cause puncture motion.

The evolution of the theory is described by the dispersionless KP hierarchy.

The generating function of correlators equals the logarithm of the tau-function of the Generalized Kontsevich Model.

Abstract

We study flows on the space of topological Landau-Ginzburg theories coupled to topological gravity. We argue that flows corresponding to gravitational descendants change the target space from a complex plane to a punctured complex plane and lead to the motion of punctures.It is shown that the evolution of the topological theory due to these flows is given by dispersionless limit of KP hierarchy. We argue that the generating function of correlators in such theories are equal to the logarithm of the tau-function of Generalized Kontsevich Model.