$\mathcal{N}=1$ Curves on Generalized Coulomb Branches

Abstract

We study the low energy effective dynamics of four-dimensional $\mathcal{N}=1$ supersymmetric gauge theories of class ${\mathcal{S}}_k$ on the generalized Coulomb branch. The low energy effective gauge couplings are naturally encoded in algebraic curves $\mathcal{X}$, which we derive for general values of the couplings and mass deformations. We then recast these IR curves $\mathcal{X}$ to the UV or M-theory form $\mathcal{C}$: the punctured Riemann surfaces on which the six-dimensional $\mathcal{N}=(1,0)$ $A_{k-1}$ SCFTs are compactified giving the class ${\mathcal{S}}_k$ theories. We find that the UV curves $\mathcal{C}$ and their corresponding meromorphic differentials take the same form as those for their mother four-dimensional $\mathcal{N}=2$ theories of class $\mathcal{S}$. They have the same poles, and their residues are functions of all the exactly marginal couplings and the bare mass parameters which we can compute exactly.

arXiv comment22 pages; to be published in Universe

References in corpus (36)

• 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
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories
• Local stabilizer codes in three dimensions without string logical operators
• Fractons
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Fracton Phases of Matter
• Branes And The Dynamics Of QCD
• The Coulomb Phase of N=2 Supersymmetric QCD
• Four-Dimensional SCFTs from M5-Branes
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Phases of N=1 supersymmetric gauge theories in four dimensions
• On the realization of chiral four-dimensional gauge theories using branes
• Brane Boxes and Branes on Singularities
• E-String Theory on Riemann Surfaces
• D-type Conformal Matter and SU/USp Quivers
• Compactifications of ADE conformal matter on a torus
• N=1 dynamics with T_N theory
• 4D Gauge Theories with Conformal Matter
• N=1 Geometries via M-theory
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• Generalized Hitchin system, Spectral curve and N=1 dynamics
• Accidental Symmetries and N=1 Duality in Supersymmetric Gauge Theory
• Punctures for Theories of Class ${\mathcal{S}}_{\Gamma }$
• Fractons and exotic symmetries from branes
• N=1 curves for trifundamentals
• Four dimensional superconformal theories from M5 branes
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• E-string Quantum Curve
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• Seiberg-Witten geometry of four-dimensional N=2 SO-USp quiver gauge theories, I
• Comments on Quivers and Fractons
• A freely generated ring for N=1 models in class S_k

Cited by in corpus (2)

• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• Aspects of 4d supersymmetric dynamics and geometry