Non-perturbative Quantum Theories and Integrable Equations

Abstract

I review the appearance of classical integrable systems as an effective tool for the description of non-perturbative exact results in quantum string and gauge theories. Various aspects of this relation: spectral curves, action-angle variables, Whitham deformations and associativity equations are considered separately demonstrating hidden parallels between topological 2d string theories and naively non-topological 4d theories. The proofs are supplemented by explicit illustrative examples.

35 pages, LaTeX, to appear in Int.J.Mod.Phys. A

References in corpus (2)

• WDVV-like equations in N=2 SUSY Yang-Mills Theory
• Cubics, Integrable Systems, and Calabi-Yau Threefolds

Cited by in corpus (10)

• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• RG Equations from Whitham Hierarchy
• The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory
• Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras
• 5d and 6d Supersymmetric Gauge Theories: Prepotentials from Integrable Systems
• Insights and Puzzles from Branes: 4d SUSY Yang-Mills from 6d Models
• On Integrable Systems and Supersymmetric Gauge Theories
• Covariance of WDVV equations
• Symplectic forms in the theory of solitons