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

We compute topological one-point functions of the chiral operator Tr phi(k) in the maximally con. ning phase of U(N) supersymmetric gauge theory. These one-point functions are polynomials in the equivariant parameter h and the parameter of instanton expansion q = Lambda(2N) and 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 diagrams of relevant functions, we find a relation among chiral one-point functions, which recursively determines the h expansion of the generating function of one-point functions. Using a result from the operator formalism of the Gromov-Witten theory, we also present a vacuum expectation value of the loop operator Tr e(it phi).