Functional renormalization group at finite density and Bose condensation

TL;DR

This paper explores the application of the functional renormalization group to finite density systems, specifically analyzing pion condensation and phase diagrams with respect to temperature and isospin chemical potential.

Contribution

It introduces a study of pion condensation using the functional renormalization group at finite density, highlighting issues with gauge invariance in local-potential approximation.

Findings

Critical chemical potential for Bose-Einstein condensation differs from the mode mass in local approximation.

The effective average action's gauge invariance is broken in the local-potential approximation.

Discussion of potential solutions to restore gauge invariance in the approximation.

Abstract

We discuss the functional renormalization group and pion condensation in the presence of a finite isospin chemical potential $\mu_I$. We calculate the phase diagram as function of temperature $T$ and $\mu_I$. While the exact effective average action is invariant under certain gauge transformations, the effective action in the local-potential approximation is not. As a consequence, the critical chemical potential $\mu_I^c$ for Bose-Einstein condensation at T=0 is no longer equal to the mass of the condensing mode. We discuss possible solutions to this problem.