Quantum Gravity on $dS_{3}$
T. R. Govindarajan, R. K. Kaul, V. Suneeta
TL;DR
This paper formulates quantum gravity on $dS_{3}$ using a Chern-Simons description and identifies the entropy-determining sector with boundary degrees of freedom on a solid torus, linking bulk quantum gravity to a boundary $SU(2)$ WZW/CFT. It derives an exact canonical partition function in the large-$k$ limit, finds the leading Bekenstein-Hawking entropy $S_0 = \frac{2\pi l}{4G}$, and uncovers a universal logarithmic correction with coefficient $-1$, consistent with dS/CFT Cardy-type analysis and with BTZ comparisons in appropriate limits. The fluctuations correspond to discrete point-mass configurations with quantized deficit angles, while the dominant background remains empty de Sitter space, aligning with entropy bounds. The results illuminate the role of boundary degrees of freedom in de Sitter entropy and reveal regime-dependent universality of the logarithmic correction.
Abstract
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.