On Born-Infeld-type higher-spin interactions and supersymmetry
Abstract
We develop a simple Lorentz-covariant construction of the Born--Infeld-type cubic interactions (s, s1, s2) of massless higher-spin fields with s + s1 + s2 derivatives in four-dimensiona flat space. For arbitrary spins s ≥ s1 ≥ s2, the vertex is formulated in terms of a conserved higher-spin current and its trace. In contrast to the famous Berends--Burgers--van Dam currents, these currents are constructed from higher-spin Weyl tensors of a single chirality, schematically J ∼ ∂ C ∂ C. Starting with a general ansatz, we derive recurrence relations fixing the current coefficients, identify the unique non-trivial conserved current after eliminating trivial (fake) vertices, and show that in the range s ≤ s1 + s2 the interaction admits a manifestly gauge-invariant representation in terms of higher-spin Weyl tensors. The construction is then extended to 𝒩=1 and 𝒩=2 supersymmetry using the corresponding off-shell superfield formalisms. In the 𝒩=1 case, we obtain the general conserved integer superspin s supercurrent with manifest supersymmetry, which is bilinear in the Weyl supertensors of superspins Y1 and Y2. For identical superfields, Y1 = Y2, this supercurrent vanishes for odd s and is in agreement with earlier results by Gates and Koutrolikos. In the 𝒩=2 case, using harmonic superspace, we construct the principal higher-spin supercurrent whose coefficients are uniquely fixed by the conservation equations. In contrast to the 𝒩=0,1 cases, for identical 𝒩=2 superfields, the corresponding vertex does not vanish. The results provide a systematic framework for Born--Infeld-type higher-spin interactions and their supersymmetric extensions.
Related
- Topological black holes of Einsteinian cubic gravity and Born-Infeld-type electrodynamics
- Thin-Shell Wormholes in Born--Infeld-Type Magnetic Spacetimes
- Model and parameter-path dependence of charged Dirac quasi-bound spectra in Born--Infeld and Euler--Heisenberg-type geometries
- Effective Lifshitz-Born-Infeld black holes from general covariance breaking
- Charged regular AdS3 black holes in a scalar-vector-tensor theory coupled to Born-Infeld electrodynamics
BibTeX
@misc{zaigraev2026borninfeldtype,
title = {{On Born-Infeld-type higher-spin interactions and supersymmetry}},
author = {Nikita Zaigraev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31652},
eprint = {2610.31652},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31652},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Born-Infeld-type higher-spin interactions and supersymmetry
AU - Nikita Zaigraev
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31652
UR - https://arxiv.org/abs/2610.31652
AB - We develop a simple Lorentz-covariant construction of the Born--Infeld-type cubic interactions (s, s_1, s_2) of massless higher-spin fields with s + s_1 + s_2 derivatives in four-dimensiona flat space. For arbitrary spins s ≥ s_1 ≥ s_2, the vertex is formulated in terms of a conserved higher-spin current and its trace. In contrast to the famous Berends--Burgers--van Dam currents, these currents are constructed from higher-spin Weyl tensors of a single chirality, schematically J ∼ ∂ C ∂ C. Starting with a general ansatz, we derive recurrence relations fixing the current coefficients, identify the unique non-trivial conserved current after eliminating trivial (fake) vertices, and show that in the range s ≤ s_1 + s_2 the interaction admits a manifestly gauge-invariant representation in terms of higher-spin Weyl tensors. The construction is then extended to 𝒩=1 and 𝒩=2 supersymmetry using the corresponding off-shell superfield formalisms. In the 𝒩=1 case, we obtain the general conserved integer superspin s supercurrent with manifest supersymmetry, which is bilinear in the Weyl supertensors of superspins Y_1 and Y_2. For identical superfields, Y_1 = Y_2, this supercurrent vanishes for odd s and is in agreement with earlier results by Gates and Koutrolikos. In the 𝒩=2 case, using harmonic superspace, we construct the principal higher-spin supercurrent whose coefficients are uniquely fixed by the conservation equations. In contrast to the 𝒩=0,1 cases, for identical 𝒩=2 superfields, the corresponding vertex does not vanish. The results provide a systematic framework for Born--Infeld-type higher-spin interactions and their supersymmetric extensions.
ER -