Instanton calculus and chiral one-point functions in supersymmetric gauge theories

We compute topological one-point functions of the chiral operator Tr φk 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 = Λ2N . 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. 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.