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 by Raghuram et al. [J. High Energy Phys. 07 (2021) 048] to be realizable only as part a larger sector $({\mathfrak{g}}^{\ensuremath{'}}\ensuremath{\supset}\mathfrak{g},{M}^{\ensuremath{'}}\ensuremath{\supset}M)$ in F-theory. To detach any reference string theoretic method construction, we utilize flavor symmetries provide compelling reasons why vast majority such $(\mathfrak{g},M)$ theories are not compatible with quantum gravity constraints, how ``automatic enhancement'' $({\mathfrak{g}}^{\ensuremath{'}},{M}^{\ensuremath{'}})$ remedies this. In first class models, ${\mathfrak{g}}^{\ensuremath{'}}=\mathfrak{g}\ensuremath{\bigoplus}\mathfrak{h}$, show that there exists an unbroken symmetry $\mathfrak{h}$ acting on matter $M$, which, if ungauged, would violate no-global-symmetries hypothesis. This argument also applies 1-form center symmetries, which govern group topology massive states representations different from those massless states. second class, find is incompatible supersymmetric strings must exist completeness