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

We compute topological one-point functions of the chiral operator Tr ϕ^k in the maximally confining phase of U(N) supersymmetric gauge theory. These one-point functions are polynomials in the equivariant parameter \hbar and the parameter of instanton expansion q=Λ^{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 \hbar 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^{itϕ}.