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Wavefunctions of AdS3 Universes and TT̅-deformed Torus Partition Functions

  • Shinji Hirano
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Abstract

We study wavefunctions of quantum gravity in asymptotically AdS3 spacetimes and their relation to TT̅-deformed torus partition functions. We show that the deformed partition function is given by an invertible integral transform of bulk wavefunctions, which implements a change of representation from the York time to its conjugate, the spatial volume. The invertibility of the transform allows the bulk wavefunction to be reconstructed from the family of TT̅-deformed partition functions. A TT̅-deformed partition function at fixed coupling is the amplitude of the bulk state in a finite-width, fixed-volume wavepacket localized at the asymptotic boundary in York time. In the CFT limit, the wavepacket localizes at the boundary, recovering the standard holographic relation. The holographic screen of a given state is the support of the integrand of the transform: at large central charge, it separates from the wavepacket and reproduces finite-cutoff holography for the sign of the coupling with complex energies, and glue-on holography for the opposite sign. In Euclidean signature, the construction arises naturally from wavefunctions of Rindler AdS3, while after a double Wick rotation it admits a Lorentzian interpretation in terms of closed AdS3 torus universes without asymptotic boundaries. We also discuss de Sitter torus universes and generalizations to other spatial topologies and higher dimensions.

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Cite

BibTeXRIS
BibTeX
@misc{hirano2026wavefunctions,
  title = {{Wavefunctions of AdS$_3$ Universes and $T\barT$-deformed Torus Partition Functions}},
  author = {Shinji Hirano},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.04665},
  eprint = {2608.04665},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.04665},
}
RIS
TY  - UNPB
TI  - Wavefunctions of AdS_3 Universes and TT̅-deformed Torus Partition Functions
AU  - Shinji Hirano
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.04665
UR  - https://arxiv.org/abs/2608.04665
AB  - We study wavefunctions of quantum gravity in asymptotically AdS_3 spacetimes and their relation to TT̅-deformed torus partition functions. We show that the deformed partition function is given by an invertible integral transform of bulk wavefunctions, which implements a change of representation from the York time to its conjugate, the spatial volume. The invertibility of the transform allows the bulk wavefunction to be reconstructed from the family of TT̅-deformed partition functions. A TT̅-deformed partition function at fixed coupling is the amplitude of the bulk state in a finite-width, fixed-volume wavepacket localized at the asymptotic boundary in York time. In the CFT limit, the wavepacket localizes at the boundary, recovering the standard holographic relation. The holographic screen of a given state is the support of the integrand of the transform: at large central charge, it separates from the wavepacket and reproduces finite-cutoff holography for the sign of the coupling with complex energies, and glue-on holography for the opposite sign. In Euclidean signature, the construction arises naturally from wavefunctions of Rindler AdS_3, while after a double Wick rotation it admits a Lorentzian interpretation in terms of closed AdS_3 torus universes without asymptotic boundaries. We also discuss de Sitter torus universes and generalizations to other spatial topologies and higher dimensions.
ER  -