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PreprintCC BY 4.0arXiv

Topological entanglement entropy in 3D gravity

  • Vijay Balasubramanian
  • Charlie Cummings
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Abstract

We derive an entropy formula for a recently proposed tensor network model of states in 3D gravity which satisfy the constraint equations of diffeomorphism invariance, and including the effects of matter. After accounting for the invertibility of the spacetime metric, we argue that this formula matches the quantum extremal surface formula (for small but finite GN), and is not restricted to time symmetric spacetimes. We derive the result via canonical quantization without relying on path integrals, and discuss an extension to compact bulk subregions.

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Cite

BibTeXRIS
BibTeX
@misc{balasubramanian2026topological,
  title = {{Topological entanglement entropy in 3D gravity}},
  author = {Vijay Balasubramanian and Charlie Cummings},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19247},
  eprint = {2609.19247},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19247},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Topological entanglement entropy in 3D gravity
AU  - Vijay Balasubramanian
AU  - Charlie Cummings
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19247
UR  - https://arxiv.org/abs/2609.19247
AB  - We derive an entropy formula for a recently proposed tensor network model of states in 3D gravity which satisfy the constraint equations of diffeomorphism invariance, and including the effects of matter. After accounting for the invertibility of the spacetime metric, we argue that this formula matches the quantum extremal surface formula (for small but finite G_N), and is not restricted to time symmetric spacetimes. We derive the result via canonical quantization without relying on path integrals, and discuss an extension to compact bulk subregions.
ER  -