Spontaneous symmetry restoration in a field theory at finite chemical potential in a toroidal topology

TL;DR

This paper investigates how finite size, temperature, and chemical potential influence spontaneous symmetry restoration in a vector field theory confined between parallel planes, using large-N limit calculations.

Contribution

It develops a method to analyze combined effects of temperature, boundaries, and chemical potential on symmetry in a toroidal topology.

Findings

Finite size and chemical potential significantly affect symmetry restoration.

Results show temperature and boundaries can induce or prevent symmetry breaking.

Large-N limit provides clear insights into phase transitions under these conditions.

Abstract

We consider the massive vector $N$-component $(\lambda\varphi^{4})_{D}$ theory defined on a Euclidean space with a toroidal topology. Using recently developed methods to perform a compactification of a $d$-dimensional subspace at finite chemical potential, we treat jointly the effects of temperature and spatial boundaries, setting forth grounds for an analysis of spontaneous symmetry restoration driven by temperature and spatial boundaries as a function of the chemical potential. We restrict ourselves to d=2, which corresponds to the heated system confined between two parallel planes (separation $L$) in dimensions D=3 and D=4. We present results, in the large-$N$ limit, which exhibit how finite size and chemical potential affect spontaneous symmetry restoration.