  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.

High Energy Physics - Theory