Anomaly-Free Spectra, Unimodular Lattices and 6D R-Symmetry Gauged Supergravity

TL;DR

This paper classifies anomaly-free 6D supergravity models with gauged U(1)_R symmetry, presenting new models and analyzing their mathematical structure to understand the constraints on consistent theories.

Contribution

It introduces eleven new anomaly-free models with specific gauge groups and explores their arithmetic and lattice properties, expanding the known landscape of consistent 6D supergravities.

Findings

Identified new models satisfying anomaly and consistency conditions.

Established that n_V ≡ 8 mod 12 is necessary and sufficient for unimodular embeddability.

Analyzed the role of D_4 Lie algebra in anomaly contributions.

Abstract

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.