Liberating Confinement from Lagrangians: 1-form Symmetries and Lines in 4d N=1 from 6d N=(2,0)

Abstract

We study confinement in 4d N=1 theories obtained by deforming 4d N=2 theories of Class S. We argue that confinement in a vacuum of the N=1 theory is encoded in the 1-cycles of the associated N=1 curve. This curve is the spectral cover associated to a generalized Hitchin system describing the profiles of two Higgs fields over the Riemann surface upon which the 6d (2,0) theory is compactified. Using our method, we reproduce the expected properties of confinement in various classic examples, such as 4d N=1 pure Super-Yang-Mills theory and the Cachazo-Seiberg-Witten setup. More generally, this work can be viewed as providing tools for probing confinement in non-Lagrangian N=1 theories, which we illustrate by constructing an infinite class of non-Lagrangian N=1 theories that contain confining vacua. The simplest model in this class is an N=1 deformation of the N=2 theory obtained by gauging $SU(3{)}^3$ flavor symmetry of the $E_6$ Minahan-Nemeschansky theory.

86 pages, many tikz figures, v2: references added

References in corpus (8)

• Generalized Global Symmetries
• Four-Dimensional SCFTs from M5-Branes
• Non-Invertible Global Symmetries and Completeness of the Spectrum
• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• Loop operators and S-duality from curves on Riemann surfaces
• Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality
• Holography, 1-Form Symmetries, and Confinement
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence

Cited by in corpus (14)

• The Branes Behind Generalized Symmetry Operators
• 2-Group Symmetries in Class S
• Symmetry TFTs for 3d QFTs from M-theory
• Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions
• Higher Symmetries of 5d Orbifold SCFTs
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• Anomalies of Generalized Symmetries from Solitonic Defects
• Disconnected 0-Form and 2-Group Symmetries
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• The Characteristic Dimension of Four-dimensional $\mathcal{N}=2$ SCFTs
• Disconnected gauge groups in the infrared
• Symmetry TFTs from String Theory
• The quantum UV-IR map for line defects in $\mathfrak{gl}(3)$-type class $S$ theories
• Aspects of 4d supersymmetric dynamics and geometry