Black Hole Horizon Edge Partition Functions

Abstract

We extend a formula for 1-loop black hole determinants by Denef, Hartnoll, and Sachdev (DHS) to spinning fields on any $(d+1)$-dimensional static spherically symmetric black hole. By carefully analyzing the regularity condition imposed on the Euclidean eigenfunctions, we reveal an unambiguous bulk-edge split in the 1-loop Euclidean partition function for tensor fields of arbitrary integer spin: the bulk part captures the "renormalized" thermal canonical partition function recently discussed in arXiv:2207.07024; the edge part is related to quasinormal modes (QNMs) that fail to analytically continue to a subset of Euclidean modes with enhanced fall-offs near the origin. Since the edge part takes the form of a path integral on $S^{d-1}$, this suggests that these are associated with degrees of freedom living on the bifurcation surface in the Lorentzian two-sided black hole geometry. For massive higher spin on static BTZ and massive vector on Nariai black holes, we find that the edge partition function is related to the QNMs with lowest overtone numbers.

27+17 pages; published version

References in corpus (5)

• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Tweaking one-loop determinants in AdS${}_3$
• Entanglement Entropy in (3+1)-d Free $U(1)$ Gauge Theory
• Entanglement entropy of gravitational edge modes
• Black Hole Scattering and Partition Functions

Cited by in corpus (9)

• Dynamical Edge Modes and Entanglement in Maxwell Theory
• Keeping matter in the loop in dS${}_3$ quantum gravity
• Is the Euclidean path integral always equal to the thermal partition function?
• Dynamical Edge Modes in $p$-form Gauge Theories
• Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics
• De Sitter entropy: on-shell versus off-shell
• Real-time observables in de Sitter thermodynamics
• De Sitter Horizon Edge Partition Functions
• Gravitons on Nariai Edges