Correlation Functions in The Itzykson-Zuber Model

TL;DR

This paper derives explicit formulas for correlation functions in the Itzykson-Zuber model, simplifying the computation of n-point functions through reduction to Gelfand-Tzetlin integrals and differential equations.

Contribution

It introduces a new method to explicitly compute 2-point and some n-point functions in the Itzykson-Zuber model using Gelfand-Tzetlin parametrization.

Findings

Explicit formulas for 2-point functions

Polynomial form of certain n-point functions

Linear differential equation for general n-point functions

Abstract

The n-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over Gelfand-Tzetlin table; integrand (for generic n) is given by linear exponential times rational function. For $n=2$ and in some cases for $n>2$ later in fact is the polinomial and this allows to give an explicit and simple expression for all 2-point and a set of n-point functions. For the most general n-point function a simple linear differential equation is constructed.