The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$

Abstract

Even though for generic $\mathcal{N}=1$ theories it is not possible to separate distinct branches of supersymmetric vacua, in this paper we study a special class of $\mathcal{N}=1$ SCFTs, these of Class ${\mathcal{S}}_k$ for which it is possible to define Coulomb and Higgs branches precisely as for the $\mathcal{N}=2$ theories of Class $\mathcal{S}$ from which they descend. We study the BPS operators that parameterise these branches of vacua using the different limits of the superconformal index as well as the Coulomb and Higgs branch Hilbert Series. Finally, with the tools we have developed, we provide a check that six dimensional $(1,1)$ Little String theory can be deconstructed from a toroidal quiver in class ${\mathcal{S}}_k$

arXiv comment58 pages

References in corpus (69)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• An Index for 4 dimensional Super Conformal Theories
• Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories
• Infinite Chiral Symmetry in Four Dimensions
• Lectures on supersymmetric gauge theories and electric-magnetic duality
• Counting chiral primaries in N=1 d=4 superconformal field theories
• The Refined Topological Vertex
• Matrix Description of M-theory on $T^5$ and $T^5/Z_2$
• Linear Dilatons, NS5-branes and Holography
• Gauge Theories and Macdonald Polynomials
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Counting Gauge Invariants: the Plethystic Program
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• S-duality and 2d Topological QFT
• Four-Dimensional SCFTs from M5-Branes
• A brief review of "little string theories"
• Matrix Description of M-theory on $T^4$ and $T^5$
• Holography for Non-Critical Superstrings
• Notes on Theories with 16 Supercharges
• Varieties of vacua in classical supersymmetric gauge theories
• Deconstructing (2,0) and Little String Theories
• Correlation Functions of Coulomb Branch Operators
• The Master Space of N=1 Gauge Theories
• Elliptic hypergeometry of supersymmetric dualities
• SQCD: A Geometric Apercu
• The Superconformal Index of the E_6 SCFT
• Exceptional Indices
• Surface Defects and Chiral Algebras
• The superconformal index of N=1 class S fixed points
• $t{t}^{\ast }$ equations, localization and exact chiral rings in 4d N=2 SCFTs
• Infrared Computations of Defect Schur Indices
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• E-String Theory on Riemann Surfaces
• On exact correlation functions in SU(N) $\mathcal{N}=2$ superconformal QCD
• Exact correlation functions in SU(2) N=2 superconformal QCD
• D-type Conformal Matter and SU/USp Quivers
• The supersymmetric index in four dimensions
• Highest Weight Generating Functions for Hilbert Series
• Hilbert Series for Moduli Spaces of Two Instantons
• Compactifications of ADE conformal matter on a torus
• The Veneziano Limit of N=2 Superconformal QCD: Towards the String Dual of N=2 SU(N_c) SYM with N_f =2 N_c
• Counting Gauge Invariant Operators in SQCD with Classical Gauge Groups
• Deconstructing (2,0) Proposals
• Little strings and T-duality
• Studying superconformal symmetry enhancement through indices
• Higgs branch, HyperKahler quotient and duality in SUSY N=2 Yang-Mills theories
• Chiral theories of class S
• Surface Defect Indices and 2d-4d BPS States
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• On elliptic genera of 6d string theories
• Supersymmetric States in M5/M2 CFTs
• Punctures for Theories of Class ${\mathcal{S}}_{\Gamma }$
• Exact Deconstruction of the 6D (2,0) Theory
• Geometry of Higgs-branch superconformal primary bundles
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• Indices for 6 dimensional superconformal field theories
• Little strings on $D_n$ orbifolds
• A freely generated ring for N=1 models in class S_k
• Deconstructing Little Strings with $\mathcal{N}=1$ Gauge Theories on Ellipsoids
• The Complete One-loop Spin Chain of N =1 SQCD
• Deconstructing Defects
• Punctures and Dynamical Systems
• Towards Deconstruction of the Type D (2,0) Theory

Cited by in corpus (8)

• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• Comments on Quivers and Fractons
• $\mathcal{N}=1$ Curves on Generalized Coulomb Branches
• Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV
• Hilbert Series of Bipartite Field Theories
• Four-dimensional $\mathcal{N}=1$ SCFTs on S-folds with T-branes and AdS/CFT correspondence
• Aspects of 4d supersymmetric dynamics and geometry