Tau functions for the Dirac operator on the Poincare' disk

TL;DR

This paper explores the correlation functions of holonomic fields on the Poincare' disk, revealing their expression in terms of Painleve' VI functions, thus linking geometric analysis with special functions.

Contribution

It establishes a novel connection between correlation functions on the Poincare' disk and Painleve' VI functions, advancing the understanding of the Dirac operator in hyperbolic geometry.

Findings

Two-point functions are expressed via Painleve' VI functions

Correlation functions are analyzed for holonomic fields on the Poincare' disk

Provides a new analytical framework for Dirac operator studies

Abstract

Correlation functions for holonomic fields on the Poincare' disk are analyzed. The two point functions are shown to be expressible in terms of Painleve' functions of type VI.