Wilson loops and chiral correlators on squashed spheres

We study chiral deformations of N = 2 and N = 4 supersymmetric gauge theories obtained by turning on tau(J) tr Phi(J) interactions with Phi the N = 2 super field. Using localization, we compute the deformed gauge theory partition function Z((tau) over right arrow vertical bar q) and the expectation value of circular Wilson loops W on a squashed four-sphere. In the case of the deformed N = 4 theory, exact formulas for Z and W are derived in terms of an underlying U(N) interacting matrix model replacing the free Gaussian model describing the N = 4 theory. Using the AGT correspondence, the tau(J)-deformations are related to the insertions of commuting integrals of motion in the four-point CFT correlator and chiral correlators are expressed as tau-derivatives of the gauge theory partition function on a finite Omega-background. In the so called Nekrasov-Shatashvili limit, the entire ring of chiral relations is extracted from the epsilon-deformed Seiberg-Witten curve. As a byproduct of our analysis we show that SU(2) gauge theories on rational Omega-backgrounds are dual to CFT minimal models.