Speaker
Description
One-loop partition functions encode leading-order quantum corrections to the gravitational path integral and can be constructed from quasinormal modes and heat kernel methods. We investigate how exact computations of these quantities can be extended beyond highly symmetric backgrounds. Trace formulas provide a powerful framework connecting spectral data of differential operators to geometric data of the underlying manifold. In this talk, I will first review how the Selberg trace formula can be used to compute the one-loop partition function of massive scalar fields in the BTZ black hole background. I will then present how we develop a method to compute one-loop partition functions on broader classes of manifolds by using the Gutzwiller trace formula. We find that there are two geometric types whose properties lead to different spectral structures in the corresponding quasinormal modes and one-loop partition functions.