  We present new evidence for the conjecture that BPS correlation functions in
the N=2 supersymmetric gauge theories are described by an auxiliary two
dimensional conformal field theory. We study deformations of the N=2
supersymmetric gauge theory by all gauge-invariant chiral operators. We
calculate the partition function of the N=2 theory on R^4 with appropriately
twisted boundary conditions. For the U(1) theory with instantons (either
noncommutative, or D-instantons, depending on the construction) the partition
function has a representation in terms of the theory of free fermions on a
sphere, and coincides with the tau-function of the Toda lattice hierarchy.
Using this result we prove to all orders in string loop expansion that the
effective prepotential (for U(1) with all chiral couplings included) is given
by the free energy of the topological string on CP^1. Gravitational descendants
play an important role in the gauge fields/string correspondence. The dual
string is identified with the little string bound to the fivebrane wrapped on
the two-sphere. We also discuss the theory with fundamental matter
hypermultiplets.
