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

Abstract

We analyze the finite temperature behaviour of massless conformally coupled scalar fields in homogeneous lens spaces S3/ℤp. High and low temperature expansions are explicitly computed and the behavior of thermodynamic quantities under thermal duality is scrutinized. The analysis of the entropy in the high-temperature limit of the different lens spaces points out the appearance of a temperature-independent contribution of topological origin to the entropy. The remaining terms are exponentially suppressed by the temperature. The topological contribution to the entropy appears as a subleading correction to the Stefan-Boltzmann term of the free energy, and 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.