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PreprintarXiv licencearXiv

An Algebraic Formulation of Thermality in Nested Rindler Wedges

  • Waheed A. Dar
  • Prince A. Ganai
  • Nirmalya Kajuri
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Abstract

Padmanabhan and Kolekar had demonstrated the phenomenon of recursive thermality in two dimensional free field theories where the Rindler vacuum appears thermal to an observer accelerated with respect to the Rindler observer. We study the same construction at an algebraic level for conformal field theories. At each step, a parent wedge is conformally mapped to a reference Minkowski spacetime, where a new right Rindler wedge and its left sibling are selected. We illustrate that under the Bisognano--Wichmann property, thermality holds at every generation: the state associated with a parent wedge becomes a KMS state when restricted to its right child. Further, using the modular structure of the wedge and its causal sibling, we identify the sibling algebra with the modular commutant and derive the corresponding recursive modular flow explicitly.

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Cite

BibTeXRIS
BibTeX
@misc{dar2026algebraic,
  title = {{An Algebraic Formulation of Thermality in Nested Rindler Wedges}},
  author = {Waheed A. Dar and Prince A. Ganai and Nirmalya Kajuri},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27007},
  eprint = {2610.27007},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27007},
}
RIS
TY  - UNPB
TI  - An Algebraic Formulation of Thermality in Nested Rindler Wedges
AU  - Waheed A. Dar
AU  - Prince A. Ganai
AU  - Nirmalya Kajuri
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.27007
UR  - https://arxiv.org/abs/2610.27007
AB  - Padmanabhan and Kolekar had demonstrated the phenomenon of recursive thermality in two dimensional free field theories where the Rindler vacuum appears thermal to an observer accelerated with respect to the Rindler observer. We study the same construction at an algebraic level for conformal field theories. At each step, a parent wedge is conformally mapped to a reference Minkowski spacetime, where a new right Rindler wedge and its left sibling are selected. We illustrate that under the Bisognano--Wichmann property, thermality holds at every generation: the state associated with a parent wedge becomes a KMS state when restricted to its right child. Further, using the modular structure of the wedge and its causal sibling, we identify the sibling algebra with the modular commutant and derive the corresponding recursive modular flow explicitly.
ER  -