Saved in:
Bibliographic Details
Main Authors: Anikeeva, Galit, Dulac, Raphaël, Wei, Zixia, Zhang, Mengyang
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.13970
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914564698800128
author Anikeeva, Galit
Dulac, Raphaël
Wei, Zixia
Zhang, Mengyang
author_facet Anikeeva, Galit
Dulac, Raphaël
Wei, Zixia
Zhang, Mengyang
contents We revisit the Hartle-Hawking wave function in AdS spacetime, where natural spatial slices are open and require an additional spacetime boundary. This leads to two constructions: a fully gravitational wave function, in which the boundary configuration is integrated over, and a partially frozen one, in which it is fixed, as in AdS/CFT. To illustrate the fully gravitational construction, we explicitly analyze it in AdS$_3$ Einstein gravity and AdS$_2$ Jackiw-Teitelboim gravity. We then evaluate the one-loop correction to the hyperbolic-ball partition function in $D$-dimensional AdS Einstein gravity, expected to give the leading contribution to the wave-function norm. We demonstrate that the fully gravitational hyperbolic ball partition function, where the boundary fluctuates, develops a nontrivial one-loop phase of $(\mp i)^{D+1}$, analogous to that of the sphere partition function in dS gravity. By contrast, the partially frozen partition function, where the boundary is fixed, remains real and positive. Motivated by this AdS comparison, we conversely investigate a partially frozen dS sphere partition function where the metric on an equator is fixed, finding that its one-loop phase cancels nontrivially. Our results suggest that the phase problem is controlled by whether the gravitational path integral is fully dynamical or partially frozen.
format Preprint
id arxiv_https___arxiv_org_abs_2605_13970
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Tale of Two Hartle-Hawking Wave Functions: Fully Gravitational vs Partially Frozen
Anikeeva, Galit
Dulac, Raphaël
Wei, Zixia
Zhang, Mengyang
High Energy Physics - Theory
General Relativity and Quantum Cosmology
We revisit the Hartle-Hawking wave function in AdS spacetime, where natural spatial slices are open and require an additional spacetime boundary. This leads to two constructions: a fully gravitational wave function, in which the boundary configuration is integrated over, and a partially frozen one, in which it is fixed, as in AdS/CFT. To illustrate the fully gravitational construction, we explicitly analyze it in AdS$_3$ Einstein gravity and AdS$_2$ Jackiw-Teitelboim gravity. We then evaluate the one-loop correction to the hyperbolic-ball partition function in $D$-dimensional AdS Einstein gravity, expected to give the leading contribution to the wave-function norm. We demonstrate that the fully gravitational hyperbolic ball partition function, where the boundary fluctuates, develops a nontrivial one-loop phase of $(\mp i)^{D+1}$, analogous to that of the sphere partition function in dS gravity. By contrast, the partially frozen partition function, where the boundary is fixed, remains real and positive. Motivated by this AdS comparison, we conversely investigate a partially frozen dS sphere partition function where the metric on an equator is fixed, finding that its one-loop phase cancels nontrivially. Our results suggest that the phase problem is controlled by whether the gravitational path integral is fully dynamical or partially frozen.
title A Tale of Two Hartle-Hawking Wave Functions: Fully Gravitational vs Partially Frozen
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2605.13970