Effective QCD Partition Function in Sectors with Non-Zero Topological Charge and Itzykson-Zuber Type Integral

TL;DR

This paper proves a conjecture linking the finite volume effective partition function of QCD with non-zero topological charge to an Itzykson-Zuber type integral, using the original integral in the proof.

Contribution

It provides a rigorous proof of the conjecture connecting QCD partition functions with Itzykson-Zuber integrals, advancing theoretical understanding.

Findings

Confirmed the conjecture for non-zero topological charge cases

Established a mathematical link between QCD partition functions and matrix integrals

Utilized the original Itzykson-Zuber integral in the proof

Abstract

It was conjectured by Jackson et.al. that the finite volume effective partition function of QCD with the topological charge $M-N$ coincides with the Itzyskon-Zuber type integral for $M\times N$ rectangular matrices. In the present article we give a proof of this conjecture, in which the original Itzykson-Zuber integral is utilized.