QCD with chemical potential on S^1 x S^3

TL;DR

This paper analyzes the phase diagram of QCD at finite temperature and chemical potential on S^1 x S^3 using one-loop perturbation theory, focusing on large N and Nf, and discusses complex gauge configurations.

Contribution

It provides analytical results for the QCD phase diagram on S^1 x S^3 at large N and Nf, including complex gauge field configurations, extending previous lattice and perturbative studies.

Findings

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

Complexified gauge configurations are essential for large N analysis

Comparison with lattice QCD results for N=2 and N=3

Abstract

In this proceedings we summarize our calculation of the phase diagram of QCD at non-zero temperature and chemical potential on S^1 x S^3 from one-loop perturbation theory [1], which is valid in the limit R << 1/Lambda, where R is the radius of S^3. We calculate several observables including the Polyakov lines and the quark number, for large number of colors N and large number of quark flavors Nf, on S^1 x S^3, and compare with results for the same system with N = 3, and with results for N=2 lattice QCD. For N > 2 the action is complex and the dominant contributions to the path integral occur in the space of complexified gauge field configurations. This results in the expectation values of the eigenvalues of the Polyakov line lying off the unit circle and out in the complex plane. This is an important issue for the lattice, and also for the calculation on S^1 x S^3 in the large N limit where we obtain analytical results using the saddle point approximation. It is thus necessary to adapt available techniques to locate the stationary solutions in the complexified gauge field configuration space.