Anomaly-Free Spectra, Unimodular Lattices and 6D R-Symmetry Gauged Supergravity
Abstract
We study the classification problem for anomaly-free 6D 𝒩=(1,0) supergravities with a gauged abelian R-symmetry and one tensor multiplet. We present eleven new models with gauge group Gnon−Abelian× U(1)R that satisfy the local Green--Schwarz factorization condition, together with several recently proposed global consistency conditions. In particular, the low-rank models we found are precisely where some of the recent enumeration literature is least directly applicable. These examples suggest that the landscape of anomaly-free gauged U(1)R supergravities may be richer than previously recognized while still remaining highly constrained. We analyze the arithmetic structure of the anomaly coefficients, including their integral pairings, embeddability into rank-two unimodular charge lattices, the characteristic-vector condition and ghost-free gauge-field conditions. We show that nV ≡ 8 pmod12 is necessary and sufficient for the unimodular embeddability in the rank-two case, when the gauge group does not contain SU(2), SU(3) and G2. For the characteristic-vector condition we verify sufficiency for the branches realized by our examples and identify a remaining branch requiring additional exclusion. We also present a detailed discussion of the contribution to the anomaly polynomial when the D4 Lie algebra is present. These results sharpen the boundary between anomaly-free 6D spectra, global-consistency constraints, and possible UV realization in string theory or F-theory.
Versions
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BibTeX
@misc{becker2026anomalyfree,
title = {{Anomaly-Free Spectra, Unimodular Lattices and 6D R-Symmetry Gauged Supergravity}},
author = {Katrin Becker and Qi You},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.17643},
eprint = {2605.17643},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.17643},
}
RIS
TY - UNPB
TI - Anomaly-Free Spectra, Unimodular Lattices and 6D R-Symmetry Gauged Supergravity
AU - Katrin Becker
AU - Qi You
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2605.17643
UR - https://arxiv.org/abs/2605.17643
AB - We study the classification problem for anomaly-free 6D 𝒩=(1,0) supergravities with a gauged abelian R-symmetry and one tensor multiplet. We present eleven new models with gauge group G_non−Abelian× U(1)_R that satisfy the local Green--Schwarz factorization condition, together with several recently proposed global consistency conditions. In particular, the low-rank models we found are precisely where some of the recent enumeration literature is least directly applicable. These examples suggest that the landscape of anomaly-free gauged U(1)_R supergravities may be richer than previously recognized while still remaining highly constrained. We analyze the arithmetic structure of the anomaly coefficients, including their integral pairings, embeddability into rank-two unimodular charge lattices, the characteristic-vector condition and ghost-free gauge-field conditions. We show that n_V ≡ 8 pmod12 is necessary and sufficient for the unimodular embeddability in the rank-two case, when the gauge group does not contain SU(2), SU(3) and G_2. For the characteristic-vector condition we verify sufficiency for the branches realized by our examples and identify a remaining branch requiring additional exclusion. We also present a detailed discussion of the contribution to the anomaly polynomial when the D_4 Lie algebra is present. These results sharpen the boundary between anomaly-free 6D spectra, global-consistency constraints, and possible UV realization in string theory or F-theory.
ER -