QCD with Chemical Potential in a Small Hyperspherical Box

TL;DR

This paper analyzes the phase structure of large N QCD with finite chemical potential on a small hyperspherical box, revealing complex eigenvalue distributions and phase transitions, and compares these results with N=3 numerical simulations.

Contribution

It provides an analytical solution for large N QCD with chemical potential on a small sphere, highlighting complex eigenvalue contours and phase transitions, and compares with finite N numerical results.

Findings

Third-order Gross-Witten transition at low temperatures as mu crosses quark energy levels

Eigenvalues of Polyakov line lie off the unit circle in the complex plane

Similar physical observables between large N theory and N=3 numerical simulations

Abstract

To leading order in perturbation theory, we solve QCD, defined on a small three sphere in the large N and Nf limit, at finite chemical potential and map out the phase diagram in the (mu,T) plane. The action of QCD is complex in the presence of a non-zero quark chemical potential which results in the sign problem for lattice simulations. In the large N theory, which at low temperatures becomes a conventional unitary matrix model with a complex action, we find that the dominant contribution to the functional integral comes from complexified gauge field configurations. For this reason the eigenvalues of the Polyakov line lie off the unit circle on a contour in the complex plane. We find at low temperatures that as mu passes one of the quark energy levels there is a third-order Gross-Witten transition from a confined to a deconfined phase and back again giving rise to a rich phase structure. We compare a range of physical observables in the large N theory to those calculated numerically in the theory with N=3. In the latter case there are no genuine phase transitions in a finite volume but nevertheless the observables are remarkably similar to the large N theory.