Quantum corrections in thermal states of fermions on anti-de Sitter space-time

TL;DR

This paper investigates the quantum corrections to the energy density and pressure of massless fermions in thermal states on Minkowski and anti-de Sitter space-times, highlighting the differences in vacuum and thermal contributions.

Contribution

It provides a detailed comparison of vacuum and thermal expectation values of the stress-energy tensor for fermions in curved space-times, emphasizing quantum corrections in AdS.

Findings

Vacuum expectation value is zero in Minkowski space.

Vacuum expectation value is nonzero in AdS space.

Thermal contributions can dominate over vacuum in certain conditions.

Abstract

We study the energy density and pressure of a relativistic thermal gas of massless fermions on four-dimensional Minkowski and anti-de Sitter space-times using relativistic kinetic theory. The corresponding quantum field theory quantities are given by components of the renormalized expectation value of the stress-energy tensor operator acting on a thermal state. On Minkowski space-time, the renormalized vacuum expectation value of the stress-energy tensor is by definition zero, while on anti-de Sitter space-time the vacuum contribution to this expectation value is in general nonzero. We compare the properties of the vacuum and thermal expectation values of the energy density and pressure for massless fermions and discuss the circumstances in which the thermal contribution dominates over the vacuum one.