The planar limit of ${\cal N}=2$ chiral correlators

TL;DR

This paper calculates the all-order planar 2- and 3-point functions of chiral primary operators in ${ m N}=2$ SQCD on $S^4$, providing a combinatorial matrix model solution and conjecturing general formulas for these correlators.

Contribution

It introduces a combinatorial approach to the planar free energy of a matrix model with complex trace terms and applies it to derive explicit correlator formulas in ${ m N}=2$ SQCD.

Findings

Derived all-order planar 2- and 3-point functions on $S^4$

Provided a combinatorial expression for the free energy of complex matrix models

Conjectured general formulas for correlators on ${ m R}^4$

Abstract

We derive the planar limit of 2- and 3-point functions of single-trace chiral primary operators of ${\cal N}=2$ SQCD on $S^4$, to all orders in the 't Hooft coupling. In order to do so, we first obtain a combinatorial expression for the planar free energy of a hermitian matrix model with an infinite number of arbitrary single and double trace terms in the potential; this solution might have applications in many other contexts. We then use these results to evaluate the analogous planar correlation functions on ${\mathbb R}^4$. Specifically, we compute all the terms with a single value of the $\zeta$ function for a few planar 2- and 3-point functions, and conjecture general formulas for these terms for all 2- and 3-point functions on ${\mathbb R}^4$.