Thermodynamics of conformal fields in topologically non-trivial space-time backgrounds

TL;DR

This paper investigates the thermodynamics of conformal scalar fields in lens spaces, revealing a topological entropy component at high temperatures and analyzing dualities between high and low temperature behaviors.

Contribution

It provides explicit high and low temperature expansions for conformal fields in lens spaces and identifies a topological nonextensive entropy contribution.

Findings

Topological entropy appears as a subleading correction at high temperatures.

High and low temperature expansions are explicitly computed.

Duality between high and low temperature behaviors is analyzed.

Abstract

We analyze the finite temperature behaviour of massless conformally coupled scalar fields in homogeneous lens spaces $S^3/{\mathbb Z}_p$. High and low temperature expansions are explicitly computed and the behavior of thermodynamic quantities under thermal duality is scrutinized. The analysis of the entropy of the different lens spaces in the high-temperature limit points out the appearance of a topological nonextensive entropy, besides the standard Stefan-Boltzmann extensive term. The remaining terms are exponentially suppressed by the temperature. The topological entropy appears as a subleading correction to the free energy that can be obtained from the determinant of the lens space conformal Laplacian operator. In the low-temperature limit the leading term in the free energy is the Casimir energy and there is no trace of any power correction in any lens space. In fact, the remaining corrections are always exponentially suppressed by the inverse of the temperature. The duality between the results of both expansions is further analyzed in the paper.