Logarithmic Corrections, Entanglement Entropy, and UV Cutoffs in de Sitter Spacetime

Abstract

It has been argued that the entropy of de Sitter space corresponds to the entanglement between disconnected regions computable by switching on a replica parameter $q$ modeled by the quotient dS$/\mathbb{Z}_q$. Within this framework, we show that the centrally-extended asymptotic symmetry algebra near the cosmic horizon is a single copy of the Virasoro algebra. The resulting density of states matches the semi-classical result of Gibbons and Hawking up to an undetermined constant that is chosen to reproduce the entanglement entropy previously found in the literature. It follows that the logarithmic quantum corrections to the Cardy entropy reproduces the known one-loop result computed in the bulk in the presence of a cutoff. The resulting entanglement entropy follows the divergent area law, where the UV cutoff is now a function of the replica parameter. Thus, as the near-horizon CFT fixes the cutoff in units of the Planck scale, the model can be viewed as a probe into whether the defect Hilbert space has a finite dimension; indeed, the limit $q\to 0$, reproduces Banks' formula. We also study the quantum corrections of the effective description of the horizon entropy by means of Liouville field theory, where the large $q$ limit corresponds to a realization of dS$_3$/CFT$_2$ correspondence matching the logarithmic corrections to three-dimensional de Sitter space obtained by computing the one-loop contribution to the quantum gravity partition function in the round three-sphere.