The $\tau$-function of the universal Whitham hierarchy, matrix models and topological field theories

TL;DR

This paper explores the universal Whitham hierarchy through the lens of topological field theories, defining its tau-function and linking algebraic orbits to topological matter models coupled with gravity.

Contribution

It introduces a tau-function for the universal Whitham hierarchy and establishes a correspondence between its algebraic orbits and topological matter models with gravity.

Findings

Defined the tau-function for the universal Whitham hierarchy

Identified algebraic orbits with topological matter models coupled with gravity

Established a connection between integrable hierarchies and topological field theories

Abstract

The universal Witham hierarchy is considered from the point of view of topological field theories. The $\tau$-function for this hierarchy is defined. It is proved that the algebraic orbits of Whitham hierarchy can be identified with various topological matter models coupled with topological gravity.