Path Integral Factorization and the Gravitational Effective Action

TL;DR

This paper explores the properties of the gravitational path integral with higher curvature terms, revealing discontinuities in temperature at saddle points and confirming entropy calculations with established methods.

Contribution

It introduces a method to analyze boundary terms and saddle points in the Euclidean gravitational path integral with higher dimension operators, extending previous results.

Findings

Saddle points with discontinuous temperature are robust against quantum corrections.

Boundary terms for microcanonical ensemble are constructed.

Entropy of Schwarzschild-de Sitter matches Wald's formula.

Abstract

We discuss the factorization and continuity properties of fields in the Euclidean gravitational path integral with higher dimension operators constructed from powers of the Riemann tensor. We construct the boundary terms corresponding to the microcanonical ensemble and show that the saddle point approximation to the path integral with a quasilocal energy constraint generally yields a saddle point with discontinuous temperature. This extends a previous result for the Euclidean Schwarzschild-de Sitter geometry in Einstein gravity and shows that it is robust against at least some types of quantum corrections from heavy fields. As an application, we compute the entropy of SdS in $\text{D}=4$ using the BTZ method. Our result matches the entropy calculated using Wald's formula.