General prescription for global U(1)'s in 6D SCFTs

We present a general prescription for determining the global U(1) symmetries of six-dimensional superconformal field theories. We use the quiverlike gauge theory description of the tensor branch to identify candidate U(1) symmetries which can act on generalized matter. The condition that these candidate U(1)’s are free of Adler-Bell-Jackiw anomalies provides bottom-up constraints for U(1)’s. This agrees with the answer obtained from symmetry breaking patterns induced by Higgs branch flows. We provide numerous examples illustrating the details of this proposal. In the F-theory realization of these theories, some of these symmetries originate from deformations of non-Abelian flavor symmetries localized on a component of the discriminant, while others come from an additional generator of the Mordell-Weil group. We also provide evidence that some of these global U(1)’s do not arise from gauge symmetries, as would happen in taking a decoupling limit of a model coupled to six-dimensional supergravity.