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PreprintCC BY 4.0arXiv

On functional classes in higher-spin theory

  • Yu. A. Tatarenko
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Abstract

The factorization over the ideal in the d-dimensional Vasiliev theory requires an accurate description of the higher-spin algebra π’œ and its twisted adjoint module π’œtw as certain functional spaces. It is shown that the conditions of π’œ to be closed under action of the Moyal star product, and of π’œtw to be a star-product π’œ-module along with some auxiliary conditions lead to properly defined free-level factorization procedure. The conditions on admissible functions have simple algebraic form; in the case of π’œ the analogous functional space has been considered by Soloviev \cite{Soloviev:2013iba}. The relation of the obtained functional classes to the locality problem in the Vasiliev theory is discussed. In particular it is observed that certain non-local expressions diverge due to properties of π’œtw while the spin-local expressions are well-defined.

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Cite

BibTeXRIS
BibTeX
@misc{tatarenko2026functional,
  title = {{On functional classes in higher-spin theory}},
  author = {Yu. A. Tatarenko},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39851},
  eprint = {2610.39851},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39851},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On functional classes in higher-spin theory
AU  - Yu. A. Tatarenko
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39851
UR  - https://arxiv.org/abs/2610.39851
AB  - The factorization over the ideal in the d-dimensional Vasiliev theory requires an accurate description of the higher-spin algebra π’œ and its twisted adjoint module π’œ^tw as certain functional spaces. It is shown that the conditions of π’œ to be closed under action of the Moyal star product, and of π’œ^tw to be a star-product π’œ-module along with some auxiliary conditions lead to properly defined free-level factorization procedure. The conditions on admissible functions have simple algebraic form; in the case of π’œ the analogous functional space has been considered by Soloviev \cite{Soloviev:2013iba}. The relation of the obtained functional classes to the locality problem in the Vasiliev theory is discussed. In particular it is observed that certain non-local expressions diverge due to properties of π’œ^tw while the spin-local expressions are well-defined.
ER  -