Flavor symmetries and automatic enhancement in the 6D supergravity swampland

We argue for the quantum-gravitational inconsistency of certain 6D N = (1, 0) supergravity theories, whose anomaly-free gauge algebra g and hypermultiplet spectrum M were observed by Raghuram et al. [J. High Energy Phys. 07 (2021) 048] to be realizable only as part of a larger gauge sector (g' superset of g, M' superset of M) in F-theory. To detach any reference to a string theoretic method of construction, we utilize flavor symmetries to provide compelling reasons why the vast majority of such (g, M) theories are not compatible with quantum gravity constraints, and how the "automatic enhancement" to (g', M') remedies this. In the first class of models, with g' = g circle plus 1, we show that there exists an unbroken flavor symmetry h acting on the matter M, which, if ungauged, would violate the no-global-symmetries hypothesis. This argument also applies to 1-form center symmetries, which govern the gauge group topology and massive states in representations different from those of massless states. In a second class, we find that g is incompatible with the flavor symmetry of certain supersymmetric strings that must exist by the completeness hypothesis.