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

TL;DR

This paper derives a formula for operator mixing of chiral primary operators in large N superconformal field theories on S^4, and applies it to compute correlators with Wilson loops, connecting to matrix models and general N=2 theories.

Contribution

It provides a general Chebyshev polynomial-based formula for operator mixing in large N superconformal theories on S^4, enabling simplified computation of correlators with Wilson loops.

Findings

Derived a general operator mixing formula using Chebyshev polynomials.

Reproduced known correlator results with Wilson loops from matrix models.

Proposed a perturbative method to relate N=2 correlators to N=4 theory results.

Abstract

We find a general formula for the operator mixing on the $\mathbb{S}^4$ of chiral primary operators (CPO) for the ${\cal N}=4$ 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 ${\cal N}=2$ superconformal field theories in perturbation theory in terms of correlators of the ${\cal N}=4$ theory.