Structure of 𝒩 = 2 superfield higher-spin abelian cubic interactions
Abstract
In this article we study the structure of the 𝒩=2 abelian higher-spin cubic (s1, s2, s2) vertices and the corresponding 𝒩=2 higher-spin supercurrents, introduced in arXiv:2408.00668. These interactions are possible only for s1 ≥ 2 s2. Conserved supercurrents are constructed as descendants of the \textit{principal supercurrent}, which is uniquely characterized by simple differential conditions and admits an explicit representation in terms of 𝒩=2 higher-spin super-Weyl tensors. We derive the analytic form of the abelian vertices and identify the corresponding analytic higher-spin 𝒩=2 supercurrents. We show that the vertex structure is fully determined by the analytic supercurrents J++α(s−1)α̇(s−1), J+α(s−1)α̇(s−2), and J̅+α(s−2)α̇(s−1). The analytic form of the vertices provides a simple framework for analyzing their component structure. As an example, we explore the component content of such interactions on the Bel--Robinson diagonal. Using the superfield inverse Noether procedure, we study higher-spin gauge transformations for the 𝒩=2 vector multiplet associated with the (s, 1, 1) interaction. In the rigid limit, for odd s these transformations reduce to the 𝒩=2 superspace generalization of zilch-type higher-spin symmetries.
Versions
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BibTeX
@misc{zaigraev2026structure,
title = {{Structure of $\mathcalN = 2$ superfield higher-spin abelian cubic interactions}},
author = {Nikita Zaigraev},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.27206},
eprint = {2605.27206},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.27206},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Structure of 𝒩 = 2 superfield higher-spin abelian cubic interactions
AU - Nikita Zaigraev
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2605.27206
UR - https://arxiv.org/abs/2605.27206
AB - In this article we study the structure of the 𝒩=2 abelian higher-spin cubic (s_1, s_2, s_2) vertices and the corresponding 𝒩=2 higher-spin supercurrents, introduced in arXiv:2408.00668. These interactions are possible only for s_1 ≥ 2 s_2. Conserved supercurrents are constructed as descendants of the \textit{principal supercurrent}, which is uniquely characterized by simple differential conditions and admits an explicit representation in terms of 𝒩=2 higher-spin super-Weyl tensors. We derive the analytic form of the abelian vertices and identify the corresponding analytic higher-spin 𝒩=2 supercurrents. We show that the vertex structure is fully determined by the analytic supercurrents J^++_α(s−1)α̇(s−1), J^+_α(s−1)α̇(s−2), and J̅^+_α(s−2)α̇(s−1). The analytic form of the vertices provides a simple framework for analyzing their component structure. As an example, we explore the component content of such interactions on the Bel--Robinson diagonal. Using the superfield inverse Noether procedure, we study higher-spin gauge transformations for the 𝒩=2 vector multiplet associated with the (s, 1, 1) interaction. In the rigid limit, for odd s these transformations reduce to the 𝒩=2 superspace generalization of zilch-type higher-spin symmetries.
ER -