Operator Mixing in Large $N$ Superconformal Field Theories on ${\mathbb{S}}^4$ and Correlators with Wilson loops

Abstract

We find a general formula for the operator mixing on the ${\mathbb{S}}^4$ of chiral primary operators (CPO) for the $\mathcal{N}=4$ theory at large $N$ in terms of Chebyshev polynomials. As an application, we compute the correlator of a CPO and a Wilson loop, reproducing an earlier result by Giombi and Pestun obtained from a two-matrix model proposal. Finally, we discuss a simple method to obtain correlators in general $\mathcal{N}=2$ superconformal field theories in perturbation theory in terms of correlators of the $\mathcal{N}=4$ theory.

15 pages, no figures

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• Three-point functions in a $\mathcal{N}=2$ superconformal gauge theory and their strong-coupling limit
• Strong coupling expansions in $\mathcal{N}=2$ quiver gauge theories
• The planar limit of $\mathcal{N}=2$ chiral correlators
• OPE coefficients in Argyres-Douglas theories
• Integrated correlators at strong coupling in an orbifold of $\mathcal{N}=4$ SYM
• Emitted Radiation and Geometry
• Wilson loop correlators at strong coupling in $\mathcal{N}=2$ quiver gauge theories
• Partition functions of non-Lagrangian theories from the holomorphic anomaly
• Defect correlators in a $\mathcal{N}=2$ SCFT at strong coupling
• Wilson loops in Large Symmetric Representations through a Double-Scaling Limit
• On topological recursion for Wilson loops in $\mathcal{N}=4$ SYM at strong coupling
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• A derivation of the planar limit of $\mathcal{N}=2$ chiral correlators
• Chiral correlators in $\mathcal{N}=2$ superconformal quivers
• Wilson loops as defects in N=2 conformal field theories
• One-point functions for doubly-holographic BCFTs and backreacting defects
• Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography