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PreprintCC BY 4.0arXiv

Constructing and Probing Three-Boundary Booklet Geometries

  • Yan Liu
  • Shaodong Zhou
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Abstract

Partially entangled thermal states (PETS) provide semiclassical families of black-hole microstates prepared through heavy shell insertions. We extend this shell-state framework and propose three-boundary partially entangled thermal states (PETS3) by replacing the two-index insertion data with a trivalent junction tensor. The corresponding bulk three-boundary booklet geometry is constrained semiclassically by the Israel junction condition, allowing us to identify candidate symmetric and mixed-orientation branches. We verify the self-consistency of this construction by counting states in the symmetric all-black-hole sector. Using a heavy-operator probe, we further estimate the detection-to-universal ratio to be ZD/ZU ≃ 3, twice the two-boundary value of 3/2. These results suggest that a fine-tuned probe localized on one boundary can test the proposed three-boundary shell state and potentially distinguish it from its two-boundary counterpart.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026constructing,
  title = {{Constructing and Probing Three-Boundary Booklet Geometries}},
  author = {Yan Liu and Shaodong Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37099},
  eprint = {2609.37099},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37099},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Constructing and Probing Three-Boundary Booklet Geometries
AU  - Yan Liu
AU  - Shaodong Zhou
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37099
UR  - https://arxiv.org/abs/2609.37099
AB  - Partially entangled thermal states (PETS) provide semiclassical families of black-hole microstates prepared through heavy shell insertions. We extend this shell-state framework and propose three-boundary partially entangled thermal states (PETS_3) by replacing the two-index insertion data with a trivalent junction tensor. The corresponding bulk three-boundary booklet geometry is constrained semiclassically by the Israel junction condition, allowing us to identify candidate symmetric and mixed-orientation branches. We verify the self-consistency of this construction by counting states in the symmetric all-black-hole sector. Using a heavy-operator probe, we further estimate the detection-to-universal ratio to be Z_D/Z_U ≃ 3, twice the two-boundary value of 3/2. These results suggest that a fine-tuned probe localized on one boundary can test the proposed three-boundary shell state and potentially distinguish it from its two-boundary counterpart.
ER  -