Quantum Gravity on $dS_{3}$

Details Quantum Gravity on $dS_{3}$ Quantum Gravity on $dS_{3}$

2002-03-23

arxiv.org/abs/hep-th/0203219v5

Class.Quant.Grav. 19 (2002) 4195-4205

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, revtex4, 1 eps figure, published version

Scientific paper

10.1088/0264-9381/19/15/320

We study quantum gravity on $dS_{3}$ using the Chern-Simons formulation of three -dimensional gravity. We derive an exact expression for the partition function for quantum gravity on $dS_{3}$ in a Euclidean path integral approach. We show that the topology of the space relevant for studying de Sitter entropy is a solid torus. The quantum fluctuations of de Sitter space are sectors of configurations of point masses taking a {\em discrete} set of values. The partition function gives the correct semi-classical entropy. The sub-leading correction to the entropy is logarithmic in horizon area, with a coefficient -1. We discuss this correction in detail, and show that the sub-leading correction to the entropy from the dS/CFT correspondence agrees with our result. A comparison with the corresponding results for the $AdS_{3}$ BTZ black hole is also presented.

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