Three-dimensional de Sitter horizon thermodynamics

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)/CFT3 correspondence.

Automated summary

The study examines the thermodynamic contributions to the three-dimensional de Sitter horizon from metric and Chern-Simons gauge field fluctuations. In the Euclidean signature, these are calculated by the gravity partition function coupled to matter semi-classically expanded about the round three-sphere saddle. The Lorentzian picture and the gravitational edge-mode theory at the de Sitter horizon are explored, drawing inspiration from topological entanglement entropy literature.