Non-Simply-Connected Symmetries in 6D SCFTs

Abstract

Six-dimensional N=(1,0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This allows us to identify the full non-Abelian group structure rather than just the algebra. The presence of torsion also modifies the center of the symmetry groups and the matter representations that can appear. This in turn affects the tensor branch of these theories. We analyze this change for a large class of superconformal theories with torsion and explicitly construct their tensor branches. Finally, we elaborate on the connection to the dual heterotic and M-theory description, in which our configurations are interpreted as generalizations of discrete holonomy instantons.

arXiv comment62 pages, 6 figures, 5 tables, 3 appendices

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• Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality
• Higher Symmetries of 5d Orbifold SCFTs
• String Universality and Non-Simply-Connected Gauge Groups in 8d
• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
• On the Swampland Cobordism Conjecture and Non-Abelian Duality Groups
• Maruyoshi-Song Flows and Defect Groups of $D_p^b(G)$ Theories
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions
• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• The Fate of Discrete 1-Form Symmetries in 6d