On the global symmetries of 6D superconformal field theories

Abstract

We study global symmetry groups of six-dimensional superconformal field theories (SCFTs). In the Coulomb branch we use field theoretical arguments to predict an upper bound for the global symmetry of the SCFT. We then analyze global symmetry groups of F-theory constructions of SCFTs with a one-dimensional Coulomb branch. While in the vast majority of cases, all of the global symmetries allowed by our Coulomb branch analysis can be realized in F-theory, in a handful of cases we find that F-theory models fail to realize the full symmetry of the theory on the Coulomb branch. In one particularly mysterious case, F-theory models realize several distinct maximal subgroups of the predicted group, but not the predicted group itself.

arXiv comment47 pages; v2: typos corrected, added the case su(6)* to the analysis of section 5 and section 6.1. v3: references added, minor changes, published version

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• Universal Features of BPS Strings in Six-dimensional SCFTs
• Higher Form Symmetries TFT in 6d
• Fission, Fusion, and 6D RG Flows
• 6d SCFTs and U(1) Flavour Symmetries
• AdS${}_7$/CFT${}_6$ with orientifolds
• Revisiting the classifications of 6d SCFTs and LSTs
• F-Theory and N=1 SCFTs in Four Dimensions
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• General Prescription for Global U(1)'s in 6D SCFTs
• Triality in Little String Theories
• Flavor Symmetry of 5d SCFTs, Part 1: General Setup
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• Non-Simply-Connected Symmetries in 6D SCFTs
• F-theory and Unpaired Tensors in 6D SCFTs and LSTs
• Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Flavor symmetries of six-dimensional $\mathcal{N}=(1,0)$ theories from AdS/CFT correspondence
• Classifying Global Symmetries of 6D SCFTs
• The Fate of Discrete 1-Form Symmetries in 6d
• Atomic Higgsings of 6D SCFTs
• Orbi-Instantons and Class $\mathcal{S}$ Theories of Type D