Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential

TL;DR

This paper derives the microscopic spectral density of the QCD Dirac operator at nonzero baryon chemical potential using a Toda lattice approach, connecting random matrix models, partition functions, and chiral Lagrangians.

Contribution

It introduces a novel method to obtain spectral densities from the replica limit of Toda lattice equations, linking various theoretical frameworks.

Findings

Spectral density expressions for one and two flavors are provided.

The approach reveals the role of bosonic partition function singularities.

Connections between random matrix models and chiral Lagrangians are established.

Abstract

The microscopic spectral density of the QCD Dirac operator at nonzero baryon chemical potential for an arbitrary number of quark flavors was derived recently from a random matrix model with the global symmetries of QCD. In this paper we show that these results and extensions thereof can be obtained from the replica limit of a Toda lattice equation. This naturally leads to a factorized form into bosonic and fermionic QCD-like partition functions. In the microscopic limit these partition functions are given by the static limit of a chiral Lagrangian that follows from the symmetry breaking pattern. In particular, we elucidate the role of the singularity of the bosonic partition function in the orthogonal polynomials approach. A detailed discussion of the spectral density for one and two flavors is given.