SU(2) Yang-Mills Theory in Savvidy Background at Finite Temperature and Chemical Potential

TL;DR

This paper calculates the one-loop energy density of SU(2) Yang-Mills theory in a Savvidy background at finite temperature and chemical potential, resolving previous instabilities and providing real-valued results.

Contribution

It extends previous analyses by including cubic and quartic fluctuations of unstable modes, ensuring a real energy density at finite temperature and chemical potential.

Findings

Energy density is real with no imaginary part.

Numerical results show energy density variation with temperature.

Unstable modes are fully accounted for in the calculation.

Abstract

The one-loop effective energy density of a pure SU(2) Yang-Mills theory in the Savvidy background, at finite temperature and chemical potential is examined with emphasis on the unstable modes. After identifying the stable and unstable modes, the stable modes are treated in the quadratic approximation. For the unstable modes, the full expansion including the cubic and the quartic terms in the fluctuations is used. The functional integrals for the unstable modes are evaluated and added to the results for the stable modes. The resulting energy density is found to be {\it{real}}, coinciding with the real part of the energy density in the quadratic approximation of earlier study. There is now {\it{no imaginary part.}} Numerical results are presented for the variation of the energy density with temperature for various choices of the chemical potential.