Perturbative Failure Near Horizons: the Rindler Example

Abstract

Quantum field theory (QFT) in curved spacetime treats a gravitational field as a classical background upon which quantum corrections may be computed. When couplings are assumed to be small, it is traditionally believed that perturbation theory yields trustworthy predictions about interacting quantum fields in such settings — this work asserts that this is not always the case. It is argued that perturbative predictions about evolution for very long times near a horizon are subject to problems of secular growth — ie. powers of small couplings come systematically together with growing functions of time. Such growth signals a breakdown of na ̈ıve perturbative calculations of late-time behaviour, regardless of how small ambient curvatures might be. Evidence is built that such breakdowns should be generic for gravitational fields, particularly those containing horizons. This work makes use of the Rindler horizon in flat Minkowski space to demonstrate an explicit example of such perturbative breakdown. A loop correction involving an IR/UV interplay is shown to result in a two-point correlation function which exhibits secular growth. This result is shown to parallel a breakdown occurring in finite temperature QFT, where problems of secular growth are known to occur. The problematic correction is then resummed, allowing for trustworthy late-time inferences. We conclude by discussing how this calculation may be relevant for predictions near black hole horizons.