6D SCFTs, center-flavor symmetries, and Stiefel-Whitney compactifications

The center-flavor symmetry of a gauge theory specifies the global form of consistent gauge and flavor bundle background field configurations. For 6D gauge theories which arise from a tensor branch deformation of a superconformal field theory (SCFT), we determine the global structure of such background field configurations, including possible continuous Abelian symmetry and R-symmetry bundles. Proceeding to the conformal fixed point, this provides a prescription for reading off the global form of the continuous factors of the zero-form symmetry, including possible nontrivial mixing between flavor and R-symmetry. As an application, we show that this global structure leads to a large class of 4D <math display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> SCFTs obtained by compactifying on a <math display="inline"><msup><mi>T</mi><mn>2</mn></msup></math> in the presence of a topologically nontrivial flat flavor bundle characterized by an ’t Hooft magnetic flux. The resulting “Stiefel-Whitney twisted” compactifications realize several new infinite families of 4D <math display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> SCFTs, and also furnish a 6D origin for a number of recently discovered rank one and two 4D <math display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></math> SCFTs.