6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications

Abstract

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 non-trivial mixing between flavor and R-symmetry. As an application, we show that this global structure leads to a large class of 4d $\mathcal{N}=2$ SCFTs obtained by compactifying on a $T^2$ in the presence of a topologically non-trivial flat flavor bundle characterized by a 't Hooft magnetic flux. The resulting "Stiefel--Whitney twisted" compactifications realize several new infinite families of 4d $\mathcal{N}=2$ SCFTs, and also furnish a 6d origin for a number of recently discovered rank one and two 4d $\mathcal{N}=2$ SCFTs.

arXiv comment69 pages + appendices, 2 figures, 9 tables, 1 attached Mathematica notebook; v2: PRD version

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• Symmetry TFTs for 3d QFTs from M-theory
• Anomalies of Generalized Symmetries from Solitonic Defects
• Disconnected 0-Form and 2-Group Symmetries
• Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons
• Higgs, Coulomb, and Hall-Littlewood
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
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• B-brane transport in anomalous (2,2) models and localization