Chiral Random Two-Matrix Theory and QCD with imaginary chemical potential

TL;DR

This paper reviews the chiral Random Two-Matrix Theory applied to QCD with imaginary chemical potential, highlighting its ability to connect lattice simulations with low energy constants and detailing eigenvalue correlations.

Contribution

It introduces a chiral Random Two-Matrix Theory framework for QCD with imaginary chemical potential, enabling extraction of low energy constants from lattice data.

Findings

Analytic formulas for density and eigenvalue correlations

Factorisation of correlation functions at large chemical potential

Simplification of weight functions into Gaussian forms

Abstract

We summarise recent results for the chiral Random Two-Matrix Theory constructed to describe QCD in the epsilon-regime with imaginary chemical potential. The virtue of this theory is that unquenched Lattice simulations can be used to determine both low energy constants Sigma and F in the leading order chiral Lagrangian, due to their respective coupling to quark mass and chemical potential. We briefly recall the analytic formulas for all density and individual eigenvalue correlations and then illustrate them in detail in the simplest, quenched case with imaginary isospin chemical potential. Some peculiarities are pointed out for this example: i) the factorisation of density and individual eigenvalue correlation functions for large chemical potential and ii) the factorisation of the non-Gaussian weight function of bi-orthogonal polynomials into Gaussian weights with ordinary orthogonal polynomials.