Black hole one-loop determinants in the large dimension limit

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.