The moduli space of vacua of N=2 class S theories

Abstract

We develop a systematic method to describe the moduli space of vacua of four dimensional $\mathcal{N}=2$ class $\mathcal{S}$ theories including Coulomb branch, Higgs branch and mixed branches. In particular, we determine the Higgs and mixed branch roots, and the dimensions of the Coulomb and Higgs components of mixed branches. They are derived by using generalized Hitchin's equations obtained from twisted compactification of 5d maximal Super-Yang-Mills, with local degrees of freedom at punctures given by (nilpotent) orbits. The crucial thing is the holomorphic factorization of the Seiberg-Witten curve and reduction of singularity at punctures. We illustrate our method by many examples including $\mathcal{N}=2$ SQCD, $T_N$ theory and Argyres-Douglas theories.

arXiv comment33 pages, 4 figures

References in corpus (38)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• N=2 dualities
• Supergravity description of field theories on curved manifolds and a no go theorem
• Solutions Of Four-Dimensional Field Theories Via M Theory
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Supersymmetric Yang-Mills Systems And Integrable Systems
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• Infinite Chiral Symmetry in Four Dimensions
• New N=2 Superconformal Field Theories in Four Dimensions
• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
• Integrable systems and supersymmetric gauge theory
• Wall-crossing, Hitchin Systems, and the WKB Approximation
• Webs of five-branes and N=2 superconformal field theories
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• On D=5 super Yang-Mills theory and (2,0) theory
• Gauge Dynamics And Compactification To Three Dimensions
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• R-Twisting and 4d/2d Correspondences
• General Argyres-Douglas Theory
• Tinkertoys for Gaiotto Duality
• The gravity duals of N=2 superconformal field theories
• Wild Quiver Gauge Theories
• Tinkertoys for the D_N series
• N=2 Supersymmetric Gauge Theories, Branes and Orientifolds
• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• M Theory And Seiberg-Witten Curves: Orthogonal and Symplectic Groups
• N=2 supersymmetric dynamics for pedestrians
• Argyres-Seiberg duality and the Higgs branch
• M5 brane and four dimensional N=1 theories I
• N=1 dynamics with T_N theory
• N=2 Moduli Spaces and N=1 Dualities for SO(n_c) and USp(2n_c) SuperQCD
• Quantum Higgs branches of isolated N=2 superconformal field theories
• Supersymmetric gauge theory, (2,0) theory and twisted 5d Super-Yang-Mills
• N=1 Geometries via M-theory
• On 6d N=(2,0) theory compactified on a Riemann surface with finite area
• Generalized Hitchin system, Spectral curve and N=1 dynamics
• On the Baryonic Branch Root of N=2 MQCD

Cited by in corpus (17)

• Bootstrapping $\mathcal{N}=2$ chiral correlators
• Magnetic quivers for rank 1 theories
• Mass-deformed $T_N$ as a linear quiver
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• Brane Webs and Magnetic Quivers for SQCD
• S-fold magnetic quivers
• Aspects of Defects in 3d-3d Correspondence
• A slow review of the AGT correspondence
• Magnetic quivers for rank 2 theories
• ADE Little String Theory on a Riemann Surface (and Triality)
• Four dimensional superconformal theories from M5 branes
• Compact Conformal Manifolds
• Hilbert series and mixed branches of $T[SU(N)]$ theory
• The (2,0) Superalgebra, Null M-branes and Hitchin's System
• Semicontinuity of 4d N=2 spectrum under renormalization group flow
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras
• Cluster Algebras and Supersymmetric Gauge Theories