Anomaly-free six-dimensional Sp(1)R-gauged supergravities
Abstract
We study anomaly constraints in six-dimensional N=(1,0) supergravity with gauged Sp(1)R symmetry, one tensor multiplet, nV vector multiplets and nH hypermultiplets. Imposing cancellation of local gravitational, gauge and mixed anomalies, together with the embedding of the anomaly coefficients in a unimodular rank-two string charge lattice, the number of vector multiplets is sharply constrained: the only allowed positive values are nV=12 and nV=96. For a neutral abelian factor, or drone, the anomaly equations force the corresponding row and column of the abelian gauge-kinetic matrix to vanish. Such a factor therefore cannot be retained as an ordinary propagating vector multiplet. For nV=96, within the class of semisimple non-R gauge algebras containing no A1 or A2 factor, the exhaustive spectra-assembly calculation yields no drone-free spectrum. For nV=12, the semisimple non-R branch is necessarily A13. In the doublet/adjoint truncation described in the text, we find 4,337,331 consistent models, classified by $102$ anomaly-vector classes. We also consider the reductive branch A2× U(1)× Sp(1)R. For A2 representations in {1,3,3̅, 6,6̅,8} and primitive U(1) charge assignments with |q|≤ 2, we find 178,538 solutions, classified by $21$ sets of anomaly vectors.
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BibTeX
@misc{becker2026anomalyfree,
title = {{Anomaly-free six-dimensional $Sp(1)_R$-gauged supergravities}},
author = {Katrin Becker and Ergin Sezgin and Qi You},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04131},
eprint = {2610.04131},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04131},
}
RIS
TY - UNPB
TI - Anomaly-free six-dimensional Sp(1)_R-gauged supergravities
AU - Katrin Becker
AU - Ergin Sezgin
AU - Qi You
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.04131
UR - https://arxiv.org/abs/2610.04131
AB - We study anomaly constraints in six-dimensional N=(1,0) supergravity with gauged Sp(1)_R symmetry, one tensor multiplet, n_V vector multiplets and n_H hypermultiplets. Imposing cancellation of local gravitational, gauge and mixed anomalies, together with the embedding of the anomaly coefficients in a unimodular rank-two string charge lattice, the number of vector multiplets is sharply constrained: the only allowed positive values are n_V=12 and n_V=96. For a neutral abelian factor, or drone, the anomaly equations force the corresponding row and column of the abelian gauge-kinetic matrix to vanish. Such a factor therefore cannot be retained as an ordinary propagating vector multiplet. For n_V=96, within the class of semisimple non-R gauge algebras containing no A_1 or A_2 factor, the exhaustive spectra-assembly calculation yields no drone-free spectrum. For n_V=12, the semisimple non-R branch is necessarily A_1^3. In the doublet/adjoint truncation described in the text, we find 4,337,331 consistent models, classified by $102$ anomaly-vector classes. We also consider the reductive branch A_2× U(1)× Sp(1)_R. For A_2 representations in {1,3,3̅, 6,6̅,8} and primitive U(1) charge assignments with |q|≤ 2, we find 178,538 solutions, classified by $21$ sets of anomaly vectors.
ER -