2-Group Symmetries of 6d Little String Theories and T-duality

Abstract

We determine the 2-group structure constants for all the six-dimensional little string theories (LSTs) geometrically engineered in F-theory without frozen singularities. We use this result as a consistency check for T-duality: the 2- groups of a pair of T-dual LSTs have to match. When the T-duality involves a discrete symmetry twist the 2-group used in the matching is modified. We demonstrate the matching of the 2-groups in several examples.

27 pages, references added, typos fixed, version to appear in Annales Henri Poincaré

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• 6d Conformal Matter
• Anomaly polynomial of general 6d SCFTs
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
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• Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
• 2-Group Symmetries and M-Theory
• Higher Symmetries of 5d Orbifold SCFTs
• Continuous Generalized Symmetries in Three Dimensions
• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations
• One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions
• 2-group global symmetries, hydrodynamics and holography
• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• The character map in (twisted differential) non-abelian cohomology
• Orbifolds by 2-groups and decomposition
• Instanton Counting, Quantum Geometry and Algebra
• Super-Spin Chains for 6D SCFTs
• Symmetry TFTs from String Theory
• Four-dimensional $\mathcal{N}=1$ SCFTs on S-folds with T-branes and AdS/CFT correspondence