Thermal field theories coupled to curved spacetime

TL;DR

This work extends thermal field theory to curved spacetime by embedding the imaginary-time formalism within Riemann-normal coordinates, enabling curvature corrections to thermal observables for scalar and fermionic fields under local thermal equilibrium. The authors derive a systematic Green's-function expansion in curvature and compute leading corrections to pressure and heat capacity, as well as curved-space extensions of Bose–Einstein condensation, U(1) current, and the Coleman–Weinberg potential. Key results include explicit curvature-induced shifts in thermodynamic quantities, a curvature-dependent critical temperature for BEC, and curvature contributions to radiative symmetry breaking, all while clarifying the domain of validity of the RNC approach. The findings offer potential implications for astrophysical objects and early-universe cosmology where spacetime curvature cannot be neglected, and provide a framework to quantify curvature effects in thermal quantum fields.

Abstract

Thermal field theory is an essential tool for comprehending various physical phenomena, including astrophysical objects such as neutron stars and white dwarfs, as well as the early stages of the universe. Nonetheless, the traditional thermal field theory formulated in Minkowski spacetime is not capable of considering the effects originating from the curved spacetime. These effects are crucial for both astrophysical and cosmological observations, making it essential to extend the domain of thermal field theory to curved spacetimes. This article's primary focus is to explore the extension of thermal field theory to curved spacetimes and its implications. We employ Riemann-normal coordinates to describe thermal field theories in curved spacetime, and we also calculate several thermodynamic observables to demonstrate the curvature corrections explicitly.