Abstract
We study chiral deformations of \( \mathcal{N}=2 \) and \( \mathcal{N}=4 \) supersymmetric gauge theories obtained by turning on τ J tr ΦJ 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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Fucito, F., Morales, J.F. & Poghossian, R. Wilson loops and chiral correlators on squashed spheres. J. High Energ. Phys. 2015, 64 (2015). https://doi.org/10.1007/JHEP11(2015)064
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DOI: https://doi.org/10.1007/JHEP11(2015)064