Minimal massive completions of partially broken higher-spin models
Abstract
The partially broken Fronsdal (PBF) model describes massless particles of arbitrary integer spin s with a gauge symmetry smaller than Fronsdal's, and differs from it only by the coefficient c of the term (p· h')2. We ask whether it admits a genuinely new massive completion. Adding a mass term and the most general local auxiliary sector with at most two derivatives, and demanding that all lower-spin sectors be non-dynamical, we show that for s=3 a single auxiliary scalar is never enough, while two scalars give a solution unique up to field redefinitions: one scalar is algebraic and its elimination exactly undoes the deformation, while the other is the auxiliary scalar of the Aragone--Deser--Yang (ADY) model. The same mechanism, with an algebraic vector, appears for s=4 and extends to arbitrary spin, and we conjecture that the resulting auxiliary content is minimal. In this minimal completion c does not survive the mass: the correlation functions of h coincide with those of the ADY model. For the Skvortsov--Vasiliev (SV) model, which belongs to the same family, we construct a massive version in which the Weyl-like symmetry survives the mass, and show that its auxiliary sector is fixed by the absence of lower-spin modes, within a general ansatz for s=3 and within a restricted one for s=4. For the partially broken SV model we obtain instead a massive completion which requires no auxiliary field beyond those of the massive SV model, and in which c survives the mass through the same contact term as in the massless theory.
Related
- The dimensional reduction of the spin-3 and spin-4 partially broken Fronsdal models
- Higher Integrability, Generalized Symmetries, and Partially Topological Field Theories
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- Beyond de Sitter: Longitudinal-Mode Instabilities and Spectral Evolution of Massive Vector Fields with Non-Minimal Curvature Coupling during Inflation
- Gauge-invariant off-shell formulations for 3D massive higher-spin supermultiplets
BibTeX
@misc{mendonca2026minimal,
title = {{Minimal massive completions of partially broken higher-spin models}},
author = {E. L. Mendonça and M. I. C. Maués},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07057},
eprint = {2611.07057},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07057},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Minimal massive completions of partially broken higher-spin models
AU - E. L. Mendonça
AU - M. I. C. Maués
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07057
UR - https://arxiv.org/abs/2611.07057
AB - The partially broken Fronsdal (PBF) model describes massless particles of arbitrary integer spin s with a gauge symmetry smaller than Fronsdal's, and differs from it only by the coefficient c of the term (p· h')^2. We ask whether it admits a genuinely new massive completion. Adding a mass term and the most general local auxiliary sector with at most two derivatives, and demanding that all lower-spin sectors be non-dynamical, we show that for s=3 a single auxiliary scalar is never enough, while two scalars give a solution unique up to field redefinitions: one scalar is algebraic and its elimination exactly undoes the deformation, while the other is the auxiliary scalar of the Aragone--Deser--Yang (ADY) model. The same mechanism, with an algebraic vector, appears for s=4 and extends to arbitrary spin, and we conjecture that the resulting auxiliary content is minimal. In this minimal completion c does not survive the mass: the correlation functions of h coincide with those of the ADY model. For the Skvortsov--Vasiliev (SV) model, which belongs to the same family, we construct a massive version in which the Weyl-like symmetry survives the mass, and show that its auxiliary sector is fixed by the absence of lower-spin modes, within a general ansatz for s=3 and within a restricted one for s=4. For the partially broken SV model we obtain instead a massive completion which requires no auxiliary field beyond those of the massive SV model, and in which c survives the mass through the same contact term as in the massless theory.
ER -