Gravitons on Nariai Edges

TL;DR

This paper demonstrates the factorization of the one-loop graviton path integral on certain geometries into bulk and edge components, revealing insights into quantum gravity and gauge theories beyond horizon geometries.

Contribution

It provides a new factorization of the graviton path integral on $S^2\times S^{d-1}$ and a compact formula for Einstein manifolds with positive cosmological constant.

Findings

Bulk equals the thermal partition function of an ideal graviton gas.

Edge factor involves path integrals over shift-symmetric vectors and scalars.

Massless scalars indicate probing beyond horizon intrinsic geometry.

Abstract

We show that, for any $d\geq 3$, the one-loop graviton path integral on $S^2\times S^{d-1}$ factorizes into bulk and edge parts. The bulk equals the thermal partition function of an ideal graviton gas in the Lorentzian Nariai geometry. The edge factor is the inverse of the path integral over two identical copies, each containing one shift-symmetric vector and three shift-symmetric scalars on $S^{d-1}$. Unlike the round $S^{d+1}$ case, all scalars are massless, indicating that graviton edge partition functions probe beyond the horizon's intrinsic geometry - in contrast to $p$-form gauge theories. In the course of this work, we obtain a compact formula for the one-loop Euclidean graviton path integral on any $\Lambda >0$ Einstein manifold.