Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and 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± and conformal results. Holography is exhibited in quasi-exact bulk-edge cancelation.

Holographic complexity and de Sitter space

“…Furthermore, in three dimensions, corrections to the cosmological horizon entropy were recently computed, finding again notable differences with respect to analogous corrections for black holes [46,47].…”

Holographic Complexity in dS$_{d+1}$

“…(3.1). 4 The WdW patch at this critical time is shown in the right panel of figure 3. We will find below that the volume of the WdW patch grows rapidly as we approach τ = τ ∞ .…”

“…Quantum corrections to this expression were evaluated in[4] 2. Let us add that yet another approach named the dS/dS correspondence[31][32][33][34][35] instead considers the correspondence between a quantum gravity in dS d+1 and two UV-cutoff CFTs which are living on dS d and coupled to each other by a d-dimensional gravitational system.…”

Characters, quasinormal modes, and Schwinger pairs in $dS_2$ with flux

“…where D 3 n+B is the degeneracy of the nth eigenvalue of D 2 . Following [6], we use the Hubbard-Stratonovich trick to perform the sum over n, writing…”

“…Nonethe-less, their action on boundary fields (3.14) allows us to find the character χ(t) directly as the trace tr e −iHt . The quasicanonical interpretation of sphere partition functions stems from the fact that the character admits a quasinormal mode (QNM) expansion [6]. This is closely related to the fact that these QNMs can be constructed algebraically as a consequence of the large symmetry group of dS [11,12,13,14].…”