General prescription for global<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>’s in 6D SCFTs
Fabio Apruzzi, Marco Fazzi, Jonathan J. Heckman, Tom Rudelius, Hao Y. Zhang
Abstract
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.