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.

arXiv comment15 pages, no figures

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