Wigner continuous-spin equations in AdSD: bosonic and fermionic cases
Abstract
We construct Wigner-like equations of motion for symmetric continuous-spin fields in anti-de Sitter space of arbitrary dimension, treating both the bosonic and fermionic cases. We generalise the classical flat-space Wigner constraints for bosonic continuous-spin fields, and for the fermionic case we adopt the equations proposed by Bekaert and Mourad as our starting point. This is achieved by covariantising the ordinary derivatives and deforming the resulting constraints so that they form a closed algebra. The construction is carried out in a metric-like formalism and yields a system of first-class constraints that define a representation of the so(2,D−1) isometry algebra, realised via the Lie-Lorentz derivative. Using these constraints, we compute the eigenvalues of the quadratic and quartic Casimir operators and compare the obtained values with Metsaev's classification of continuous-spin representations for both the bosonic and fermionic cases. A crucial algebraic role is played by special operators of the (super)algebra Howe-dual to the Lorentz subalgebra so(1,D−1): the sl(2) Casimir operator in the bosonic case, and the Casimir's ghost of the osp(1|2) superalgebra in the fermionic case. Both objects naturally organise the constraint algebra and ensure its consistency.
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BibTeX
@misc{astrakhantsev2026wigner,
title = {{Wigner continuous-spin equations in $\mathbfAdS_D$: bosonic and fermionic cases}},
author = {Lev N. Astrakhantsev and Anastasia A. Golubtsova and Mikhail A. Podoinitsyn},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.12537},
eprint = {2606.12537},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.12537},
}
RIS
TY - UNPB
TI - Wigner continuous-spin equations in AdS_D: bosonic and fermionic cases
AU - Lev N. Astrakhantsev
AU - Anastasia A. Golubtsova
AU - Mikhail A. Podoinitsyn
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2606.12537
UR - https://arxiv.org/abs/2606.12537
AB - We construct Wigner-like equations of motion for symmetric continuous-spin fields in anti-de Sitter space of arbitrary dimension, treating both the bosonic and fermionic cases. We generalise the classical flat-space Wigner constraints for bosonic continuous-spin fields, and for the fermionic case we adopt the equations proposed by Bekaert and Mourad as our starting point. This is achieved by covariantising the ordinary derivatives and deforming the resulting constraints so that they form a closed algebra. The construction is carried out in a metric-like formalism and yields a system of first-class constraints that define a representation of the so(2,D−1) isometry algebra, realised via the Lie-Lorentz derivative. Using these constraints, we compute the eigenvalues of the quadratic and quartic Casimir operators and compare the obtained values with Metsaev's classification of continuous-spin representations for both the bosonic and fermionic cases. A crucial algebraic role is played by special operators of the (super)algebra Howe-dual to the Lorentz subalgebra so(1,D−1): the sl(2) Casimir operator in the bosonic case, and the Casimir's ghost of the osp(1|2) superalgebra in the fermionic case. Both objects naturally organise the constraint algebra and ensure its consistency.
ER -