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 AdS4/CFT3 correspondence.
Highlights
This paper explores properties of massless quantum fields on a three-dimensional de Sitter background
We explore thermodynamic contributions to the three-dimensional de Sitter horizon originating from metric and Chern-Simons gauge field fluctuations
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
Summary
This paper explores properties of massless quantum fields on a three-dimensional de Sitter background. Due to the absence of local degrees of freedom in three-dimensional gravity, such a theory can always be brought back to an Einstein theory with a cosmological constant through local field redefinitions of the metric From this perspective, integrating out massless or light fields, or some more general conformal matter theory, is interesting in that one can affect the details of (1.2) which are of a more non-local nature. Of particular interest is whether the logarithmic term and further subleading terms in (1.2) have a simple Lorentzian interpretation One hope that such a link exists comes from literature on what is known as topological entanglement entropy [31, 32], which is a finite contribution to the vacuum entanglement entropy between disconnected regions of space in Chern-Simons theory or some more general topological field theory. In the second part of our discussion, we investigate a Lorentzian interpretation for the purely gravitational expression (1.2) by viewing the gravitational theory as a complexified Chern-Simons theory
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