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PreprintCC BY 4.0arXiv

A UV-Finite Refinement of the Ryu-Takayanagi Relation in AdS3/CFT2

  • Philipp Dorau
  • Albert Much
  • Leonardo Sangaletti
  • Rainer Verch
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Abstract

We establish a refined Ryu--Takayanagi (RT) relation in AdS3/CFT2 using \emph{relative entropy} as the central object, in place of the ultraviolet-divergent von Neumann entanglement entropy. Adapting Hollands' exact result for the chiral relative entropy to a diamond region, we express the boundary relative entropy between the vacuum and a coherent state as a Schwarzian functional, which the Fefferman--Graham dictionary identifies with the asymptotic data of a Bañados geometry; the rigidity of three-dimensional gravity promotes this boundary identification to the bulk. To linear order in the metric perturbation, the relative entropy then equals the variation of the RT geodesic length divided by 4GN. The construction rests only on the Bisognano--Wichmann/Borchers theorem and the holographic dictionary, giving a UV-finite, operator-algebraic counterpart to the RT relation.

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Cite

BibTeXRIS
BibTeX
@misc{dorau2026uvfinite,
  title = {{A UV-Finite Refinement of the Ryu-Takayanagi Relation in AdS$_3$/CFT$_2$}},
  author = {Philipp Dorau and Albert Much and Leonardo Sangaletti and Rainer Verch},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.27915},
  eprint = {2606.27915},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.27915},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A UV-Finite Refinement of the Ryu-Takayanagi Relation in AdS_3/CFT_2
AU  - Philipp Dorau
AU  - Albert Much
AU  - Leonardo Sangaletti
AU  - Rainer Verch
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2606.27915
UR  - https://arxiv.org/abs/2606.27915
AB  - We establish a refined Ryu--Takayanagi (RT) relation in AdS_3/CFT_2 using \emph{relative entropy} as the central object, in place of the ultraviolet-divergent von Neumann entanglement entropy. Adapting Hollands' exact result for the chiral relative entropy to a diamond region, we express the boundary relative entropy between the vacuum and a coherent state as a Schwarzian functional, which the Fefferman--Graham dictionary identifies with the asymptotic data of a Bañados geometry; the rigidity of three-dimensional gravity promotes this boundary identification to the bulk. To linear order in the metric perturbation, the relative entropy then equals the variation of the RT geodesic length divided by 4G_N. The construction rests only on the Bisognano--Wichmann/Borchers theorem and the holographic dictionary, giving a UV-finite, operator-algebraic counterpart to the RT relation.
ER  -