Wilson Loops and Chiral Correlators on Squashed Sphere

Abstract

We study chiral deformations of $\mathcal{N}=2$ and $\mathcal{N}=4$ supersymmetric gauge theories obtained by turning on ${\tau }_J\mathrm{tr}{\Phi }^J$ interactions with $\Phi$ the $\mathcal{N}=2$ superfield. Using localization, we compute the deformed gauge theory partition function $Z(\vec{\tau }|q)$ 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 ${\tau }_J$-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.

33 pages, 2 figure, in this version we have added two new references and a detailed comparison with the results obtained in one of these two

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Cited by in corpus (22)

• Correlation Functions of Coulomb Branch Operators
• Renormalization Group Flows on Line Defects
• The Exact Bremsstrahlung Function in N=2 Superconformal Field Theories
• Non-perturbative approaches to the quantum Seiberg-Witten curve
• Spin Impurities, Wilson Lines and Semiclassics
• On the large R-charge $\mathcal{N}=2$ chiral correlators and the Toda equation
• A slow review of the AGT correspondence
• A Solvable Deformation of Quantum Mechanics
• Bootstrapping 4d $\mathcal{N}=2$ gauge theories: the case of SQCD
• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Two-point correlators in non-conformal $\mathcal{N}=2$ gauge theories
• Laplace-difference equation for integrated correlators of operators with general charges in $\mathcal{N}=4$ SYM
• N=2 SUSY gauge theories on S^4
• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• The Bremsstrahlung function of $\mathcal{N}=2$ SCQCD
• Wilson Loops and Chiral Correlators on Squashed Spheres
• Conformal field theories on deformed spheres, anomalies, and supersymmetry
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Wilson loops and its correlators with chiral operators in $\mathcal{N}=2,4$ SCFT at large $N$
• Comments on Higher Rank Wilson Loops in $\mathcal{N}=2^{\ast }$
• A note on chiral trace relations from qq-characters
• Matrix models for extremal and integrated correlators of higher rank