Wilson loops and chiral correlators on squashed spheres

Abstract

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Abstract

We study chiral deformations of ...... and ...... supersymmetric gauge theories obtained by turning on [tau] ^sub J^ tr [Phi]^sup J^ interactions with [Phi] the ...... superfield. Using localization, we compute the deformed gauge theory partition function ...... and the expectation value of circular Wilson loops W on a squashed four-sphere. In the case of the deformed ...... 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 ...... theory. Using the AGT correspondence, the [tau] ^sub 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 -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.