Finite volume partition functions and Itzykson-Zuber integrals

TL;DR

This paper derives finite volume QCD partition functions for arbitrary quark masses using generalized Itzykson-Zuber integrals, extending previous results to complex and rectangular matrices and conjecturing topological charge effects.

Contribution

It introduces a generalized Itzykson-Zuber integral for complex matrices and extends finite volume QCD partition function calculations to arbitrary quark masses and topological charges.

Findings

Derived finite volume QCD partition functions for arbitrary quark masses.

Extended Itzykson-Zuber integral to complex and rectangular matrices.

Proposed a conjecture for topological charge dependence.

Abstract

We find the finite volume QCD partition function for arbitrary quark masses. This is a generalization of a result obtained by Leutwyler and Smilga for equal quark masses. Our result is derived in the sector of zero topological charge using a generalization of the Itzykson-Zuber integral appropriate for arbitrary complex matrices. We present a conjecture regarding the result for arbitrary topological charge which reproduces the Leutwyler-Smilga result in the limit of equal quark masses. We derive a formula of the Itzykson-Zuber type for arbitrary {\em rectangular} complex matrices, extending the result of Guhr and Wettig obtained for {\em square} matrices.