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Table of contents
1 Introduction and summary
1.1 Four-dimensional N = 2 gauge theories
1.2 Toda conformal field theory
1.3 Supersymmetric localization on S2
1.4 AGT correspondence and extended operators
1.5 Two-dimensional N = (2, 2) dualities
2 Two-dimensional N = (2, 2) gauge theories
2.1 Introduction
2.2 N = (2, 2) gauge theories on S2
2.3 Localization of the path integral
2.4 Coulomb branch
2.5 Higgs branch representation
2.6 Gauge theory/Toda correspondence (omitted)
2.7 Seiberg duality (omitted)
2.8 Discussion
2.A Notations and conventions
2.B Supersymmetry transformations on S2
2.C Supersymmetric configurations
2.D One-loop determinants
2.E One-loop running of FI parameter
2.F Factorization for any N = (2, 2) gauge theory
2.G Vortex partition function
2.H SU(N) partition function in various limits (omitted)
3 AGT for surface operators
3.1 Introduction and conclusions
3.2 Surface operators as Toda degenerates
3.3 SQED and Toda fundamental degenerate
3.4 SQCD and Toda antisymmetric degenerate
3.5 SQCDA and Toda symmetric degenerate
3.6 Quivers and multiple Toda degenerates
4 Two-dimensional gauge theory dualities
4.1 Introduction
4.2 Seiberg duality as momentum conjugation
4.3 SQCDA dualities: crossing and conjugation
4.4 Dualities for quivers
4.A SQCD vortex partition functions
4.B SQCDA vortex partition functions
5 Toda conformal field theory
5.1 W algebra
5.2 Braiding matrices
5.3 Braiding kernel
5.4 Toda CFT correlators
5.5 Fusion rules
5.6 Irregular punctures
