Towards All-Order Locality in the Higher-Spin Holomorphic Zero-Form Sector
Abstract
This work addresses the construction of local interaction vertices in the holomorphic zero-form sector obtained from Vasiliev equations. We focus on a requirement on zero-form vertices, previously proposed in a less restrictive form in arXiv:2208.02004, which, together with spinor spin-locality, guarantees space-time spin-locality. Necessary and sufficient conditions on the holomorphic one-form sector vertices are derived that ensure the existence of holomorphic zero-form vertices satisfying this requirement. As a concrete demonstration, the proposed scheme is applied to compute the spin-local holomorphic η2 zero-form sector vertex, a result that goes beyond previous work where only spinor spin-locality was established. These findings lay the groundwork for a systematic all-order construction of local vertices in higher-spin theory.
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BibTeX
@misc{valerev2026towards,
title = {{Towards All-Order Locality in the Higher-Spin Holomorphic Zero-Form Sector}},
author = {D. A. Valerev},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24956},
eprint = {2609.24956},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24956},
}
RIS
TY - UNPB
TI - Towards All-Order Locality in the Higher-Spin Holomorphic Zero-Form Sector
AU - D. A. Valerev
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24956
UR - https://arxiv.org/abs/2609.24956
AB - This work addresses the construction of local interaction vertices in the holomorphic zero-form sector obtained from Vasiliev equations. We focus on a requirement on zero-form vertices, previously proposed in a less restrictive form in arXiv:2208.02004, which, together with spinor spin-locality, guarantees space-time spin-locality. Necessary and sufficient conditions on the holomorphic one-form sector vertices are derived that ensure the existence of holomorphic zero-form vertices satisfying this requirement. As a concrete demonstration, the proposed scheme is applied to compute the spin-local holomorphic η^2 zero-form sector vertex, a result that goes beyond previous work where only spinor spin-locality was established. These findings lay the groundwork for a systematic all-order construction of local vertices in higher-spin theory.
ER -