Instanton counting and the chiral ring relations in supersymmetric gauge theories

We compute topological one-point functions of the chiral operator Tr phi(k) in the maximally confining phase of U(N) supersymmetric gauge theory. These chiral one-point functions are of particular interest from gauge/string theory correspondence, since they are related to the equivariant Gromov-Witten theory of P-1. By considering the power sums of Jucys-Murphy elements in the class algebra of the symmetric group we can derive a combinatorial identity that leads the relations among chiral one-point functions. Using the operator formalism of free fermions, we also compute the vacuum expectation value of the loop operator < Tr e(it phi)> which gives the generating function of the one-point functions.