In AdS the fully gravitational Hartle-Hawking wave function acquires a nontrivial one-loop phase while the partially frozen version stays real and positive; a partially frozen de Sitter sphere shows phase cancellation.
One-loop Partition Functions of 3D Gravity
13 Pith papers cite this work, alongside 245 external citations. Polarity classification is still indexing.
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abstract
We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and graviton excitations are computed explicitly using heat kernel techniques. We obtain precisely the result anticipated by Brown and Henneaux: the partition function includes a sum over "boundary excitations" of AdS3, which are the Virasoro descendants of empty Anti-de Sitter space. This result also allows us to compute the one-loop corrections to the Euclidean action of the BTZ black hole as well its higher genus generalizations.
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The Hartle-Hawking state for toroidal quantum cosmologies is expressed in the Langlands decomposition as a sum over zeta zeros whose near-singularity dynamics follow the Hilbert-Pólya Hamiltonian and as a Möbius average of CFT partition functions.
Near-extremal BTZ and warped BTZ in TMG receive log-T corrections from Schwarzian and rotational zero modes whose full-geometry eigenvalues match the throat after non-normalizable eigenfunction corrections and BC specification.
Using worldline formalism and geometric quantization, the partition function for 3D gravity with matter on thermal AdS3 is computed via equivariant localization, reproducing the Wilson spool and conjecturing the all-orders result.
Timelike geodesic-integrated Wightman functions in dS are dual to bulk-operator correlators with a linear combination of an OPE block and its Casimir partner.
Stress-tensor deformations of QFTs are mapped to gravitational actions at metric saddles, with bidirectional examples and an induced Newton constant from the one-loop effective action of a massive scalar.
The paper shows that Euclidean axion wormholes remain regular and stable in AdS3 for any mouth radius to AdS radius ratio and across topologies, with computable actions that can be included in the 3D gravitational path integral.
Spinning states scaled with central charge cancel negative densities in 3D gravity, reinterpreted as bulk defects or overspinning BTZ quotients of AdS3 that preserve the gap but exhibit causal pathologies.
One-loop partition function from boundary graviton zero modes in the near-horizon AdS2 x S1 geometry produces logarithmic corrections to the semiclassical entropy of near-extremal black holes in New Massive Gravity.
Field theory models with Robin boundary conditions and modular invariance reproduce zero-winding holographic superconductor results in 2D CFTs and interpret fractional vortices via a Little-Parks toy model.
Schwarzian modes emerge from the general solution of BTZ perturbations at finite temperature with no rotational modes present, and are equivalently obtained via a Kerr-Schild construction that connects to the double copy.
Quantum analysis of AdS3 supergravity path integrals at low temperature shows near-horizon region inequivalent to BTZ and sharpens near-extremal versus near-BPS distinctions.
Lecture notes deliver a self-contained pedagogical overview of worldsheet strings in AdS3 with NSNS flux, summarizing 25 years of results with emphasis on spectrally flowed correlation functions.
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M\"obius randomness in the Hartle-Hawking state
The Hartle-Hawking state for toroidal quantum cosmologies is expressed in the Langlands decomposition as a sum over zeta zeros whose near-singularity dynamics follow the Hilbert-Pólya Hamiltonian and as a Möbius average of CFT partition functions.
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Spinning States and Unitarity in 3D Gravity
Spinning states scaled with central charge cancel negative densities in 3D gravity, reinterpreted as bulk defects or overspinning BTZ quotients of AdS3 that preserve the gap but exhibit causal pathologies.