Seiberg-Witten Theory and Integrable Systems

Abstract

We summarize recent results on the resolution of two intimately related problems, one physical, the other mathematical. The first deals with the resolution of the non-perturbative low energy dynamics of certain N=2 supersymmetric Yang-Mills theories. We concentrate on the theories with one massive hypermultiplet in the adjoint representation of an arbitrary gauge algebra G. The second deals with the construction of Lax pairs with spectral parameter for certain classical mechanics Calogero-Moser integrable systems associated with an arbitrary Lie algebra G. We review the solution to both of these problems as well as their interrelation.

30 pages, Based on Lectures delivered at Edinburgh and Kyoto

References in corpus (11)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Introduction to Seiberg-Witten Theory and its Stringy Origin
• Elliptic Calogero-Moser system from two dimensional current algebra
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• Singular Monopoles and Supersymmetric Gauge Theories in Three Dimensions
• Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras
• Calogero-Moser and Toda Systems for Twisted and Untwisted Affine Lie Algebras
• Branes and integrability in the N=2 SUSY YM theory
• A Conjectured R-Matrix

Cited by in corpus (11)

• Integrability in QCD and beyond
• Partition Functions of Matrix Models as the First Special Functions of String Theory I. Finite Size Hermitean 1-Matrix Model
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• Seiberg-Witten Geometries Revisited
• Integrability, Seiberg-Witten Models and Picard-Fuchs Equations
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• Finding and solving Calogero-Moser type systems using Yang-Mills gauge theories
• The Dn Ruijsenaars-Schneider model
• Slavnov determinants, Yang-Mills structure constants, and discrete KP
• Matrix Model and Stationary Problem in Toda Chain
• Non-Abelian monopole equations with zero curvature and self-dual Yang-Mills theories