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PreprintCC BY 4.0arXiv

Finite Modular Hamiltonians and Their Singular Limits

  • Panyinyan Li
  • Jun Tao
  • Haitang Yang
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Abstract

Using the open solid torus as a finite parent, we revisit modular flow for spherical regions in conformal field theory. Its nonsingular angular evolution gives finite modular generators in a very simple form, while an exact conformal map to a cavity frame recovers the Rindler, CHM, and stationary-source ball constructions as singular limits. The same finite parent also provides a regular completion of the center obstruction in the complexified ball flow. Charged, Dirac, and inhomogeneous scalar examples are given.

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Cite

BibTeXRIS
BibTeX
@misc{li2026finite,
  title = {{Finite Modular Hamiltonians and Their Singular Limits}},
  author = {Panyinyan Li and Jun Tao and Haitang Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20180},
  eprint = {2610.20180},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20180},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Finite Modular Hamiltonians and Their Singular Limits
AU  - Panyinyan Li
AU  - Jun Tao
AU  - Haitang Yang
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20180
UR  - https://arxiv.org/abs/2610.20180
AB  - Using the open solid torus as a finite parent, we revisit modular flow for spherical regions in conformal field theory. Its nonsingular angular evolution gives finite modular generators in a very simple form, while an exact conformal map to a cavity frame recovers the Rindler, CHM, and stationary-source ball constructions as singular limits. The same finite parent also provides a regular completion of the center obstruction in the complexified ball flow. Charged, Dirac, and inhomogeneous scalar examples are given.
ER  -