Three-dimensional de Sitter horizon thermodynamics. (English) Zbl 1476.81090
Summary: 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 \( \mathrm{AdS}_4/ \mathrm{CFT}_3\) correspondence.
MSC:
| 81T28 | Thermal quantum field theory |
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 58J28 | Eta-invariants, Chern-Simons invariants |
Keywords:
Chern-Simons theories; classical theories of gravity; field theories in lower dimensions; AdS-CFT correspondenceReferences:
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