Supersymmetric Localization on dS: Sum over topologies

TL;DR

This paper computes the exact non-perturbative quantum gravity partition function on the static patch of 3d de Sitter space using supersymmetric localization in the Chern-Simons formulation, addressing divergences and higher spin extensions.

Contribution

It introduces a supersymmetric localization approach to 3d de Sitter quantum gravity, providing the first exact non-perturbative partition function in this setting.

Findings

Exact partition function obtained for 3d de Sitter gravity

Analysis of divergences in the theory

Discussion of higher spin gravity implications

Abstract

We find the exact quantum gravity partition function on the static patch of 3d de Sitter spacetime. We have worked in the Chern Simons Formulation of 3d Gravity. To obtain a non-perturbative result, we supersymmetrized the Chern Simons action and used the technique of supersymmetric localization. We have obtained an exact non-perturbative result for the spin-2 gravity case. We comment on the divergences present in the theory. We also comment on higher spin gravity theories and analyse the nature of divergences present in such theories.