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± and conformal results. Holography is exhibited in quasi-exact bulk-edge cancelation.
Highlights
As seen by local inhabitants [1,2,3,4,5,6,7] of a cosmology accelerated by a cosmological constant, the observable universe is evolving towards a semiclassical equilibrium state asymptotically indistin√guishable from a de Sitter static patch, enclosed by a horizon of area A = Ωd−1 d−1,∝ 1/ Λ, with the de Sitter universe globally in its Euclidean vacuum state
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
We can split up the integrals by introducing an IR regulator: ZPI = i−Ps ZG Zchar, ZG
Summary
As seen by local inhabitants [1,2,3,4,5,6,7] of a cosmology accelerated by a cosmological constant, the observable universe is evolving towards a semiclassical equilibrium state asymptotically indistin√guishable from a de Sitter static patch, enclosed by a horizon of area A = Ωd−1 d−1,. The semiclassical equilibrium state locally maximizes the observable entropy at a value S semiclassically given by [2] S = log Z , (1.1). Where Z = e−SE[g,··· ] is the effective field theory Euclidean path integral, expanded about the round sphere saddle related by Wick-rotation (D.12) to the de Sitter universe of interest. In particular there is no invariant information contained in the tree-level S(0) other than its value, which in the low-energy effective field theory merely represents a renormalized coupling constant; an input parameter. To give a simple example, discussed in more a b c
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