Integrable structure in supersymmetric gauge theories with massive hypermultiplets

Abstract

We study the quantum moduli space of vacua of $N=2$ supersymmetric $SU(N_c)$ gauge theories coupled to $N_f$ flavors of quarks in the fundamental representation. We identify the moduli space of the $N_c=3$ and $N_f=2$ massless case with the full spectral curve obtained from the Lax representation of the Goryachev-Chaplygin top. For the case with {\it massive} quarks, we present an integrable system where the corresponding hyperelliptic curve parametrizing the Laurent solution coincides with that of the moduli space of $N_c=3$ with $N_f=0,1,2$. We discuss possible generalizations of the integrable systems relevant to gauge theories with $N_c\ne 3$ and general $N_f$.

11 pages, latex, no figures

References in corpus (9)

• Supersymmetric Yang-Mills Systems And Integrable Systems
• Integrability and Seiberg-Witten Exact Solution
• Integrable systems and supersymmetric gauge theory
• On the Quantum Moduli Space of Vacua of $N=2$ Supersymmetric $SU(N_c)$ Gauge Theories
• Integrability and Seiberg-Witten Theory: Curves and Periods
• Prepotentials of $N=2$ Supersymmetric Gauge Theories and Soliton Equations
• Whitham-Toda hierarchy and N = 2 supersymmetric Yang-Mills theory
• Integrable Structures in Supersymmetric Gauge and String Theory
• Integrability and Seiberg-Witten theory

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• Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras
• N=2 supersymmetric gauge theories with massive hypermultiplets and the Whitham hierarchy
• 5d and 6d Supersymmetric Gauge Theories: Prepotentials from Integrable Systems
• Integrable Hierarchies and Contact Terms in u-plane Integrals of Topologically Twisted Supersymmetric Gauge Theories
• Solutions to the reflection equation and integrable systems for N=2 SQCD with classical groups
• Whitham Deformations of Seiberg-Witten Curves for Classical Gauge Groups
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models