On the 6d origin of discrete additional data of 4d gauge theories

Abstract

Starting with a choice of gauge algebras, specification of a 4d gauge theory involves additional data, namely the gauge groups and the discrete theta angles. Equivalently, one needs to specify the set of charges of allowed line operators. In this note, we study how these additional data are represented in 6d, when the 4d theory in question is an N=4 super Yang-Mills theory or an N=2 class S theory. We will see that the Z_N symmetry of the so-called T_N theory plays an important role. As a byproduct, we will find that the superconformal index of class S theories can be refined so that it can give 2d q-deformed Yang-Mills theory with different gauge groups associated to the same gauge algebra.

18 pages; v2: minor corrections

References in corpus (4)

• Reading between the lines of four-dimensional gauge theories
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Heisenberg Groups and Noncommutative Fluxes
• Loop operators and S-duality from curves on Riemann surfaces

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• Higher Symmetries of 5d Orbifold SCFTs
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• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Anomalies of Non-Invertible Symmetries in (3+1)d
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
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• Undoing decomposition
• A slow review of the AGT correspondence
• M-theoretic Genesis of Topological Phases
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• Decomposition in diverse dimensions
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Reflections on the Matter of 3d $\mathcal{N}=1$ Vacua and Local $Spin(7)$ Compactifications
• Non-Simply-Connected Symmetries in 6D SCFTs
• Argyres-Douglas Theories in Class S Without Irregularity
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• Quantum toroidal algebras and solvable structures in gauge/string theory
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• Star shaped quivers with flux
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• Decomposition and the Gross-Taylor string theory
• Geometric Approach to 3D Interfaces at Strong Coupling
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• 1-form Symmetries of 4d N=2 Class S Theories
• Lens space index and global properties for 4d N = 2 models
• Branes and DAHA Representations
• Generalized symmetry constraints on deformed 4d (S)CFTs
• Electric-magnetic Duality of Abelian Gauge Theory on the Four-torus, from the Fivebrane on T2 x T4, via their Partition Functions
• Symmetry TFTs from String Theory