De Sitter Horizon Edge Partition Functions

TL;DR

This paper investigates the structure of edge partition functions in de Sitter space, revealing their composition from shift-symmetric fields and proposing a brane interpretation.

Contribution

It provides a detailed analysis of the $rak{so}(d)$ structure of edge partition functions for symmetric tensors and Einstein gravity in de Sitter space.

Findings

Edge partition functions involve shift-symmetric vector and scalar fields.

Analysis applies to massive and massless symmetric tensors in any $d \,\geq\, 3$.

Suggests a brane interpretation for the edge degrees of freedom.

Abstract

One-loop $S^{d+1}$ path integrals were shown to factorize into two parts: a bulk thermal ideal gas partition function in a $dS_{d+1}$ static patch and an edge partition function associated with degrees of freedom living on $S^{d-1}$. Here, we analyze the $\mathfrak{so}(d)$ structure of the edge partition functions for massive and massless totally symmetric tensors of arbitrary rank in any $d\geq 3$. For linearized Einstein gravity on $S^{d+1}$, we find that the edge partition function receives contributions from shift-symmetric vector and scalar fields on $S^{d-1}$, suggesting a possible interpretation in terms of an embedded $S^{d-1}$ brane.