Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity

Abstract

In this note we compute the 1-loop partition function of spin-s fields on Euclidean de Sitter space S2n+1 using the quasinormal mode method. Instead of computing the quasinormal mode frequencies from scratch, we use the analytic continuation prescription LAdS → iLdS, appearing in the dS/CFT correspondence, and Wick rotate the normal mode frequencies of fields on thermal AdS2n+1 into the quasinormal mode frequencies of fields on de Sitter space. We compare the quasinormal mode and heat kernel methods of calculating 1-loop determinants, finding exact agreement, and furthermore explicitly relate these methods via a sum over the conformal dimension. We discuss how the Wick rotation of normal modes on thermal AdS2n+1 can be generalized to calculating 1-loop partition functions on the thermal spherical quotients S2n+1/Zp. We further show that the quasinormal mode frequencies encode the group theoretic structure of the spherical spacetimes in question, analogous to the analysis made for thermal AdS in [1-3].