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Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions. (English) Zbl 1521.81335

Summary: 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 \(\mathrm{sl}(n)\) 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, \(\mathrm{AdS}^\pm\) and conformal results. Holography is exhibited in quasi-exact bulk-edge cancelation.

MSC:

81T45 Topological field theories in quantum mechanics
83C57 Black holes
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83C45 Quantization of the gravitational field
81T20 Quantum field theory on curved space or space-time backgrounds
81T13 Yang-Mills and other gauge theories in quantum field theory
81T11 Higher spin theories

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