On Krichever tau-function and Verlinde formula

TL;DR

This paper explores the Krichever tau-function's properties and its application to two-dimensional quantum gravity, establishing a connection with the Verlinde formula and discussing extensions to Liouville theory.

Contribution

It provides a new proof linking the Krichever tau-function with the Verlinde formula in minimal gravity and discusses potential generalizations.

Findings

Krichever tau-function relates to minimal gravity

Verlinde formula is directly connected to the tau-function

Extensions to complex Liouville theory are considered

Abstract

We remind the definition and main properties of the Krichever quasiclassical tau-function, and turn to the application of these formulas for recent studies of two-dimensional quantum gravity. We show, that in the case of minimal gravity it turns to be directly related with the Verlinde formula for minimal models, giving in particular case its one more direct proof. Generalizations for continuous "complex Liouville" theory are also briefly discussed.