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On consistency of the interacting (anti)holomorphic higher-spin sector.

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Title: On consistency of the interacting (anti)holomorphic higher-spin sector.
Authors: Korybut, A. V.1 (AUTHOR) akoribut@gmail.com
Source: European Physical Journal C -- Particles & Fields. Aug2025, Vol. 85 Issue 8, p1-26. 26p.
Subjects: Mathematical physics, Hypothesis
Abstract: In the recently proposed generating systems for the (anti)holomorphic sector of the 4d higher spin theory (Didenko in JHEP 10:191, 2022. https://doi.org/10.1007/JHEP10(2022)191. arXiv:2209.01966 [hep-th]) and for the off-shell higher spin theory in generic dimension (Didenko and Korybut in Phys Rev D 108(8):086031, 2023. https://doi.org/10.1103/PhysRevD.108.086031. arXiv:2304.08850 [hep-th]. [Erratum: Phys Rev D 109(6):069901 (2024)]) locality was achieved due to a peculiar limiting star product. Even though the generating systems exhibit all-order locality, the product itself encounters uncertainties when functions from specific classes are multiplied. This fact leads to the absence of the Leibniz rule for the differential operator acting on the auxiliary variables z and, hence, its ambiguous definition in the generating equations. We identify the gap in the original proof of consistency associated with this freedom. Nonetheless the generating systems proposed in Didenko (2022) and Didenko and Korybut (2023) are perfectly consistent as shown by direct computations on the resulting vertices. Considering specific orderings of fields we show that consistency rests on the star-exchange-like identities for the limiting star product formulated and proved here. Connection with the 4d Vasiliev theory is discussed. [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+C+--+Particles+%26+Fields%22">European Physical Journal C -- Particles & Fields</searchLink>. Aug2025, Vol. 85 Issue 8, p1-26. 26p.
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  Data: In the recently proposed generating systems for the (anti)holomorphic sector of the 4d higher spin theory (Didenko in JHEP 10:191, 2022. https://doi.org/10.1007/JHEP10(2022)191. arXiv:2209.01966 [hep-th]) and for the off-shell higher spin theory in generic dimension (Didenko and Korybut in Phys Rev D 108(8):086031, 2023. https://doi.org/10.1103/PhysRevD.108.086031. arXiv:2304.08850 [hep-th]. [Erratum: Phys Rev D 109(6):069901 (2024)]) locality was achieved due to a peculiar limiting star product. Even though the generating systems exhibit all-order locality, the product itself encounters uncertainties when functions from specific classes are multiplied. This fact leads to the absence of the Leibniz rule for the differential operator acting on the auxiliary variables z and, hence, its ambiguous definition in the generating equations. We identify the gap in the original proof of consistency associated with this freedom. Nonetheless the generating systems proposed in Didenko (2022) and Didenko and Korybut (2023) are perfectly consistent as shown by direct computations on the resulting vertices. Considering specific orderings of fields we show that consistency rests on the star-exchange-like identities for the limiting star product formulated and proved here. Connection with the 4d Vasiliev theory is discussed. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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