Matrix Models and QCD with Chemical Potential

TL;DR

This paper reviews the application of Random Matrix Models to QCD with chemical potential, connecting symmetry-based models to field theory and lattice results, and distinguishing phenomenological and exact spectral results.

Contribution

It introduces a unified framework linking matrix models, QCD with chemical potential, and chiral perturbation theory, including new spectral results and comparisons to lattice data.

Findings

Analytic spectral results for complex and symplectic matrix models

Matching of matrix model spectra with chiral perturbation theory

Comparison of matrix model predictions with lattice simulations

Abstract

The Random Matrix Model approach to Quantum Chromodynamics (QCD) with non-vanishing chemical potential is reviewed. The general concept using global symmetries is introduced, as well as its relation to field theory, the so-called epsilon regime of chiral Perturbation Theory (echPT). Two types of Matrix Model results are distinguished: phenomenological applications leading to phase diagrams, and an exact limit of the QCD Dirac operator spectrum matching with echPT. All known analytic results for the spectrum of complex and symplectic Matrix Models with chemical potential are summarised for the symmetry classes of ordinary and adjoint QCD, respectively. These include correlation functions of Dirac operator eigenvalues in the complex plane for real chemical potential, and in the real plane for imaginary isospin chemical potential. Comparisons of these predictions to recent Lattice simulations are also discussed.