Seiberg-Witten Curves and Integrable Systems

Abstract

This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of Seiberg-Witten curves in terms of corresponding integrable models.

17 pages, LaTeX; Talk at the Edinburgh conference "Integrability: the Seiberg-Witten and Whitham Equations", 14-19 September 1998

Cited by in corpus (42)

• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• Integrability in QCD and beyond
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Small Instantons, Little Strings and Free Fermions
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• On Combinatorial Expansions of Conformal Blocks
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• M-Theory of Matrix Models
• Non-perturbative approaches to the quantum Seiberg-Witten curve
• Towards a proof of AGT conjecture by methods of matrix models
• Check of AGT Relation for Conformal Blocks on Sphere
• Magnetic expansion of Nekrasov theory: the SU(2) pure gauge theory
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• Complex Geometry of Matrix Models
• Matrix models with hard walls: Geometry and solutions
• The periodic and open Toda lattice
• Cluster Toda chains and Nekrasov functions
• String Theory or Field Theory?
• On a family of KP multi-line solitons associated to rational degenerations of real hyperelliptic curves and to the finite non-periodic Toda hierarchy
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• Seiberg-Witten Theory and Calogero-Moser Systems
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Duality in Integrable Systems and Generating Functions for New Hamiltonians
• The Dn Ruijsenaars-Schneider model
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• Whittaker vectors for $\mathcal{W}$-algebras from topological recursion
• Higher Toda Mechanics and Spectral Curves
• New results in $\mathcal{N}=2$ theories from non-perturbative string
• Generalized Toda mechanics associated with classical Lie algebras and their reductions
• Light-cone SU(2) Yang-Mills theory and conformal mechanics
• The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves
• Instantons, Hilbert Schemes and Integrability
• Matrix Model and Stationary Problem in Toda Chain
• Various aspects of Whitham times
• Landau's Last Paper and its Impact on Developments in Mathematics, Physics and Other Disciplines in New Millennium
• The Lattice Equations of the Toda Type with an Interaction between a Few Neighborhoods
• Strict versions of various matrix hierarchies related to SL(n)-loops and their combinations
• Seiberg-Witten Theory and Topological Recursion
• Correlation functions and spectral curves in models of minimal gravity