On Microscopic Origin of Integrability in Seiberg-Witten Theory

Abstract

We discuss microscopic origin of integrability in Seiberg-Witten theory, following mostly the results of hep-th/0612019, as well as present their certain extension and consider several explicit examples. In particular, we discuss in more detail the theory with the only switched on higher perturbation in the ultraviolet, where extra explicit formulas are obtained using bosonization and elliptic uniformization of the spectral curve.

24 pages, 1 figure, LaTeX, based on the talks at 'Geometry and Integrability in Mathematical Physics', Moscow, May 2006; 'Quarks-2006', Repino, May 2006; Twente conference on Lie groups, December 2006 and 'Classical and Quantum Integrable Models', Dubna, January 2007

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• On non-conformal limit of the AGT relations
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• On Combinatorial Expansions of Conformal Blocks
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• Melting Crystal, Quantum Torus and Toda Hierarchy
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• Free fermions, W-algebras and isomonodromic deformations
• Strong versus Weak Coupling Confinement in N=2 Supersymmetric QCD
• Seiberg-Witten Theory and Extended Toda Hierarchy
• Non Abelian gauge theories, prepotentials and Abelian differentials
• Tau-functions for Quiver Gauge Theories
• Residue Formulas for Prepotentials, Instanton Expansions and Conformal Blocks
• Instanton Counting and Matrix Model
• Integrable structure of melting crystal model with two q-parameters
• Instanton Counting and Dielectric Branes
• Extended $5d$ Seiberg-Witten Theory and Melting Crystal
• On two-dimensional quantum gravity and quasiclassical integrable hierarchies
• Thermodynamic limit of random partitions and dispersionless Toda hierarchy
• Geometric transitions, double scaling limits and gauge theories
• Integrable structure of melting crystal model with external potentials