Quasinormal bulk-edge characters of gravitons in Nariai geometry

TL;DR

This paper computes the graviton partition function in Nariai geometry using quasinormal modes, showing agreement with heat kernel results and identifying an edge contribution in the spectrum.

Contribution

It introduces a quasinormal mode approach to evaluate graviton partition functions and isolates the edge character contribution in Nariai geometry.

Findings

Quasinormal mode spectrum reproduces known one-loop determinants.

Edge character contribution can be extracted from quasinormal modes.

Agreement with heat kernel calculations confirms the method's validity.

Abstract

In this paper, we evaluate the character partition function of gravitons in the Nariai geometry using quasinormal modes. Employing the Denef-Hartnoll-Sachdev (DHS) prescription, we compute the bulk partition function from the spectrum of quasinormal frequencies. We demonstrate that the quasinormal partition function agrees with the bulk one-loop determinant of gravitons on $S^2 \times S^2$, as obtained via the heat kernel method. Furthermore, we isolate the contribution of the edge character from the full one-loop partition function on $S^2 \times S^2$, and provide remarks on the possible origin of this edge contribution in the quasinormal mode framework.