# Black hole one-loop determinants in the large dimension limit

## TL;DR

This paper computes one-loop determinants for gravitons in high-dimensional Schwarzschild black holes, revealing a connection to heat kernel expansions and supporting a membrane model of black holes at large dimensions.

## Contribution

It introduces a method to calculate one-loop determinants for tensor and vector fluctuations in large-dimensional black holes using quasinormal modes, linking results to lower-dimensional heat kernel expansions.

## Key findings

- One-loop determinants match heat kernel curvature expansion predictions.
- Quasinormal modes depend on a fiducial mass parameter Δ.
- Supports a membrane picture for black holes in large dimensions.

## Abstract

We calculate the contributions to the one-loop determinant for transverse traceless gravitons in an $n+3$-dimensional Schwarzschild black hole background in the large dimension limit, due to the $SO(n+2)$-type tensor and vector fluctuations, using the quasinormal mode method. Accordingly we find the quasinormal modes for these fluctuations as a function of a fiducial mass parameter $\Delta$. We show that the behavior of the one-loop determinant at large $\Delta$ accords with a heat kernel curvature expansion in one lower dimension, lending further evidence towards a membrane picture for black holes in the large dimension limit.