Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions

TL;DR

This paper calculates the exact one-loop corrected de Sitter entropy for quantum gravity theories, relating it to bulk and edge partition functions, and explores connections to topological strings and higher-spin gravity.

Contribution

It introduces a universal relation between sphere partition functions and bulk-edge spectra, providing exact results for higher-spin gravity and linking de Sitter entropy to topological string partition functions.

Findings

Exact one-loop de Sitter entropy for quantum gravity models.

All-loop results for 3D higher-spin gravity as an sl(n) Chern-Simons theory.

De Sitter vacua entropy related to topological string partition functions.

Abstract

Motivated by the prospect of constraining microscopic models, we calculate the exact one-loop corrected de Sitter entropy (the logarithm of the sphere partition function) for every effective field theory of quantum gravity, with particles in arbitrary spin representations. In doing so, we universally relate the sphere partition function to the quotient of a quasi-canonical bulk and a Euclidean edge partition function, given by integrals of characters encoding the bulk and edge spectrum of the observable universe. Expanding the bulk character splits the bulk (entanglement) entropy into quasinormal mode (quasiqubit) contributions. For 3D higher-spin gravity formulated as an sl($n$) Chern-Simons theory, we obtain all-loop exact results. Further to this, we show that the theory has an exponentially large landscape of de Sitter vacua with quantum entropy given by the absolute value squared of a topological string partition function. For generic higher-spin gravity, the formalism succinctly relates dS, AdS$^\pm$ and conformal results. Holography is exhibited in quasi-exact bulk-edge cancelation.