One-loop effective action of the CPN-1model at large μβ

In this note we consider a non-linear, large-NCPN-1 sigma model on a finite size interval with periodic boundary conditions, at finite temperature and chemical potential in the regime of beta mu large. Our goal is to extend previous calculations and obtain the coefficients of the derivative expansion of the one-loop effective action in the region of beta mu large by carrying out the appropriate analytical continuation. This calculation complements previous results and allows us to conclude that the ground state remains homogeneous in this regime as long as it is assumed to be a slowly varying function of the spatial coordinates. While this is reasonable at the two extremes of small or large chemical potential, for intermediate values of the chemical potential and small enough temperature, one might expect (by analogy with other models) that lower energy crystalline solutions may exist. In this case a simple derivative expansion, like the one discussed here, would need to be modified in order to capture these features. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

This study investigates the derivative expansion coefficients of the one-loop effective action for a non-linear large-NCPN-1 sigma model under high temperature and chemical potential conditions on a finite size interval. The findings suggest that the ground state remains homogeneous in regimes of small or large chemical potential, but lower energy crystalline solutions may exist in regions with intermediate chemical potential and low temperature.