We compute topological one-point functions of the chiral operator Tr ϕ k in the maximally confining phase of N = 1 U (N ) supersymmetric gauge theory, which is obtained from N = 2 theory by turning on a tree level superpotential W (Φ).Localization theorem for toric action allows us to express these one-point functions as polynomials in the equivariant parameter and the parameter of instanton expansion q = Λ 2N . The chiral one-point functions are of particular interest from gauge/string theory correspondence, since they are related to the Gromov-Witten theory of P 1 . Based on a combinatorial identity that gives summation formula over Young diagram of relevant functions, we find a relation among chiral onepoint functions, which recursively determines the expansion of the generating function of one-point functions.

Abstract. This is an expository paper which has two parts. In the first part, we study quiver varieties of affine A-type from a combinatorial point of view. We present a combinatorial method for obtaining a closed formula for the generating function of Poincaré polynomials of quiver varieties in rank 1 cases. Our main tools are cores and quotients of Young diagrams. In the second part, we give a brief survey of instanton counting in physics, where quiver varieties appear as moduli spaces of instantons, focusing on its combinatorial aspects.

No abstract