Supersymmetric gauge theory, (2,0) theory and twisted 5d Super-Yang-Mills

Abstract

Twisted compactification of the 6d N=(2,0) theories on a punctured Riemann surface give a large class of 4d N=1 and N=2 gauge theories, called class S. We argue that nonperturbative dynamics of class S theories are described by 5d maximal Super-Yang-Mills (SYM) twisted on the Riemann surface. In a sense, twisted 5d SYM might be regarded as a "Lagrangian" for class S theories on R^{1,2} times S^1. First, we show that twisted 5d SYM gives generalized Hitchin's equations which was proposed recently. Then, we discuss how to identify chiral operators with quantities in twisted 5d SYM. Mesons, or holomorphic moment maps, are identified with operators at punctures which are realized as 3d superconformal theories T_rho[G] coupled to twisted 5d SYM. "Baryons" are identified qualitatively through a study of 4d N=2 Higgs branches. We also derive a simple formula for dynamical superpotential vev which is relevant for BPS domain wall tensions. With these tools, we examine many examples of 4d N=1 theories with several phases such as confining, Higgs, and Coulomb phases, and show perfect agreements between field theories and twisted 5d SYM. Spectral curve is an essential tool to solve generalized Hitchin's equations, and our results clarify the physical information encoded in the curve.

73 pages, 4 figures. v2:Published version

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• Mass-deformed $T_N$ as a linear quiver
• A review of the T_N theory and its cousins
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• Aspects of Defects in 3d-3d Correspondence
• Liberating Confinement from Lagrangians: 1-form Symmetries and Lines in 4d N=1 from 6d N=(2,0)
• Charting Class ${\mathcal{S}}_k$ Territory
• A slow review of the AGT correspondence
• Chiral theories of class S
• New N=1 Dualities from M5-branes and Outer-automorphism Twists
• A search for minimal 4d N=1 SCFT
• The moduli space of vacua of N=2 class S theories
• Four dimensional superconformal theories from M5 branes
• $\mathcal{N}=1$ superconformal theories with $D_N$ blocks
• Star shaped quivers with flux
• Taming Supersymmetric Defects in 3d-3d Correspondence
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Infinitely many N=1 dualities from $m+1-m=1$
• Adjoint Reidemeister torsions from wrapped M5-branes
• Hilbert series and mixed branches of $T[SU(N)]$ theory
• Coulomb Branches of Star-Shaped Quivers
• The (2,0) Superalgebra, Null M-branes and Hitchin's System
• 5D SYM on 3D Deformed Spheres
• Gauging and Decoupling in 3d $\mathcal{N}=2$ dualities
• The Geometry of SUSY Enhancement
• $\mathcal{N}=2$ Argyres-Douglas theories, $\mathcal{N}=1$ SQCD and Seiberg duality
• Supersymmetric domain walls in maximal 6D gauged supergravity III