Three-dimensional de Sitter horizon thermodynamics

TL;DR

This paper investigates the thermodynamics of three-dimensional de Sitter horizons by analyzing metric and gauge field fluctuations, proposing an edge-mode theory, and exploring complexified Chern-Simons models with implications for holography.

Contribution

It introduces a novel edge-mode theory for de Sitter horizons and extends the analysis to complexified Chern-Simons theories, connecting horizon thermodynamics with topological field theories.

Findings

Derived thermodynamic contributions from metric and gauge fluctuations.

Proposed a complexified chiral Wess-Zumino-Witten model as the edge theory.

Analyzed complex Abelian Chern-Simons theories to understand edge modes.

Abstract

We explore thermodynamic contributions to the three-dimensional de Sitter horizon originating from metric and Chern-Simons gauge field fluctuations. In Euclidean signature these are computed by the partition function of gravity coupled to matter semi-classically expanded about the round three-sphere saddle. We investigate a corresponding Lorentzian picture - drawing inspiration from the topological entanglement entropy literature - in the form of an edge-mode theory residing at the de Sitter horizon. We extend the discussion to three-dimensional gravity with positive cosmological constant, viewed (semi-classically) as a complexified Chern-Simons theory. The putative gravitational edge-mode theory is a complexified version of the chiral Wess-Zumino-Witten model associated to the edge-modes of ordinary Chern-Simons theory. We introduce and solve a family of complexified Abelian Chern-Simons theories as a way to elucidate some of the more salient features of the gravitational edge-mode theories. We comment on the relation to the AdS$_4$/CFT$_3$ correspondence.