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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.17643 |
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Table of Contents:
- We study the classification problem for anomaly-free 6D $\mathcal N=(1,0)$ supergravities with a gauged abelian R-symmetry and one tensor multiplet. We present eleven new models with gauge group $G_{\mathrm{non-Abelian}}\times U(1)_R$ 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 $n_V \equiv 8 \pmod{12}$ is necessary and sufficient for the unimodular embeddability in the rank-two case. 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.