Flavor Symmetries and Automatic Enhancement in the 6d Supergravity Swampland

We argue for the quantum-gravitational inconsistency of certain 6d $\mathcal{N}=(1,0)$ supergravity theories, whose anomaly-free gauge algebra $\mathfrak{g}$ and hypermultiplet spectrum $M$ were observed in arxiv:2012.01437 to be realizable only as part of a larger gauge sector $(\mathfrak{g}' \supset \mathfrak{g}, M' \supset M)$ 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 $(\mathfrak{g},M)$ theories are not compatible with quantum gravity constraints, and how the "automatic enhancement" to $(\mathfrak{g}', M')$ remedies this. In the first class of models, with $\mathfrak{g}' = \mathfrak{g} \oplus \mathfrak{h}$, we show that there exists an unbroken flavor symmetry $\mathfrak{h}$ 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 than those of massless states. In a second class, we find that $\mathfrak{g}$ is incompatible with the flavor symmetry of certain BPS strings that must exist by the Completeness Hypothesis.

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