We review the study of the relation between integrable many-body systems and gauge
theories. We show that the degrees of freedom of integrable systems are related to the …

We consider the AGT relation (Alday et al., 2009 [1]), expressing conformal blocks for the
Virasoro and W-algebras in terms of Nekrasov's special functions, in the simplest case of the …

We suggested in 2009 that the Nekrasov function with one non-vanishing deformation
parameter epsilon is obtained by the standard Seiberg–Witten (SW) contour-integral …

We study the dual descriptions recently discovered for the Seiberg–Witten theory in the
presence of surface operators. The Nekrasov partition function for a four-dimensional N= 2 …

We give a concise summary of the impressive recent development unifying a number of
different fundamental subjects. The quiver Nekrasov functions (generalized hypergeometric …

The interpretation of exact results on the low-energy limit of 4D N= 2 supersymmetric Yang-
Mills theory in the language of 1D integrable system of particles is discussed. The Riemann …

A matrix model approach to proof of the AGT relation is briefly reviewed. It starts from the
substitution of conformal blocks by the Dotsenko–Fateev β-ensemble averages and …

We present a summary of what is currently known about of the AGT relations for conformal
blocks with the additional insertion of the simplest degenerate operator, and a special …

The AGT conjecture claims an equivalence of conformal blocks in 2d CFT and sums of
Nekrasov functions (instantonic sums in 4d SUSY gauge theory). The conformal blocks can …

Construction of the prepotential in the Seiberg-Witten theory/the Whitham hierarchy is
presented. Consideration begins from the notion of quasi-classical τ-functions, which uses …