Functional renormalization group at finite density and Bose condensation

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.

Comments: 14 pages. 5 Figs. 2nd version matches published version. Fig.3 improved. Refs. added. Typos fixed