On the quantum moduli space of vacua of N = 2 supersymmetric SU(Nc) gauge theories

1995/05/14 by Amihay Hanany, Yaron Oz · 9 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Gauge theory #Instanton #Moduli #Moduli of algebraic curves #Moduli space #Monodromy #Quantum #Quantum Chromodynamics and Particle Interactions #Singularity #hep-th

paper · pdf · doi:10.1016/0550-3213(95)00376-4

published as Nucl.Phys.B452:283-312,1995 · 35 pages, latex

arxiv created 1995/05/14 · openalex publication_date 1995/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We construct families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of N=2 supersymmetric SU(N_c) gauge theories coupled to N_f flavors of quarks in the fundamental representation. The quantum moduli spaces for N_f < N_c are determined completely by imposing R-symmetry, instanton corrections and the proper classical singularity structure. These curves are verified by residue and weak coupling monodromy calculations. The quantum moduli spaces for N_f≥ N_c theories are parameterized and their general structure is worked out using residue calculations. Global symmetry considerations suggest a complete description of them. The results are supported by weak coupling monodromy calculations. The exact metrics on the quantum moduli spaces as well as the exact spectrum of stable massive states are derived. We find an example of a novel symmetry of a quantum moduli space: Invariance under the exchange of a moduli parameter and the bare mass. We apply our method for the construction of the quantum moduli spaces of vacua of N=1 supersymmetric theories in the coulomb phase.

Citations

• Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
• Supersymmetry algebras that include topological charges
• Electric-magnetic duality in supersymmetric non-Abelian gauge theories
• Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD

Cited by

• Duality symmetries for N = 2 supersymmetric QCD with vanishing β-functions
• SuperconformalRcharges and dyon multiplicities inN=2gauge theories
• Picard–Fuchs equations and Whitham hierarchy in N=2 supersymmetric SU(r+1) Yang–Mills theory
• One-instanton prepotentials from WDVV equations in N=2 supersymmetric SU(4) Yang–Mills theory
• Discrete Painlevé system and the double scaling limit of the matrix model for irregular conformal block and gauge theory
• Supersymmetric N=2 gauge theory with arbitrary gauge group
• Chiral rings, singularity theory and electric-magnetic duality
• Differential equations for scaling relation in N=2 supersymmetric SU(2) Yang–Mills theory coupled with massive hypermultiplet
• Classification of 4d N =2 gauge theories