# Wilson loops and chiral correlators on squashed spheres

Journal of High Energy Physics, Nov 2015

Abstract We study chiral deformations of $$\mathcal{N}=2$$ and $$\mathcal{N}=4$$ supersymmetric gauge theories obtained by turning on τ J tr Φ J interactions with Φ the $$\mathcal{N}=2$$ superfield. Using localization, we compute the deformed gauge theory partition function $$Z\left(\left.\overrightarrow{\tau}\right|q\right)$$ and the expectation value of circular Wilson loops W on a squashed four-sphere. In the case of the deformed $$\mathcal{N}=4$$ 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 $$\mathcal{N}=4$$ theory. Using the AGT correspondence, the τ J -deformations are related to the insertions of commuting integrals of motion in the four-point CFT correlator and chiral correlators are expressed as τ-derivatives of the gauge theory partition function on a finite Ω-background. In the so called Nekrasov-Shatashvili limit, the entire ring of chiral relations is extracted from the ϵ-deformed Seiberg-Witten curve. As a byproduct of our analysis we show that SU(2) gauge theories on rational Ω-backgrounds are dual to CFT minimal models.

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F. Fucito, J. F. Morales, R. Poghossian. Wilson loops and chiral correlators on squashed spheres, Journal of High Energy Physics, 2015, 64, DOI: 10.1007/JHEP11(2015)064