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PreprintCC BY 4.0arXiv

OPE and correlation functions in a generally covariant form

  • Arpit Das
  • Anatoly Konechny
  • Naveen Balaji Umasankar
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Abstract

In this paper we consider some general aspects of Euclidean conformal field theories on curved spaces of dimension D≥ 3. We first look at the OPE of scalar primary fields on conformally flat spaces. Extending the results of \cite{Konechny:2026bqg}, we give a general construction of the descendants' contributions to the OPE in the scalar channel. We then discuss CFTs on non-conformally flat spaces in the ambient space formalism. We investigate the short-distance behaviour of three-point functions on such spaces using the general ansatz proposed by Parisini, Skenderis, and Withers \cite{Parisini:2022wkb, Parisini:2023nbd}. We find that some additional corrections need to be added to the ansatz to ensure the existence of a local covariant OPE.

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Cite

BibTeXRIS
BibTeX
@misc{das2026correlation,
  title = {{OPE and correlation functions in a generally covariant form}},
  author = {Arpit Das and Anatoly Konechny and Naveen Balaji Umasankar},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28743},
  eprint = {2608.28743},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28743},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - OPE and correlation functions in a generally covariant form
AU  - Arpit Das
AU  - Anatoly Konechny
AU  - Naveen Balaji Umasankar
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28743
UR  - https://arxiv.org/abs/2608.28743
AB  - In this paper we consider some general aspects of Euclidean conformal field theories on curved spaces of dimension D≥ 3. We first look at the OPE of scalar primary fields on conformally flat spaces. Extending the results of \cite{Konechny:2026bqg}, we give a general construction of the descendants' contributions to the OPE in the scalar channel. We then discuss CFTs on non-conformally flat spaces in the ambient space formalism. We investigate the short-distance behaviour of three-point functions on such spaces using the general ansatz proposed by Parisini, Skenderis, and Withers \cite{Parisini:2022wkb, Parisini:2023nbd}. We find that some additional corrections need to be added to the ansatz to ensure the existence of a local covariant OPE.
ER  -