Exact correlation functions in SU(2) N=2 superconformal QCD

TL;DR

The paper constructs an exact, non-perturbative description of the coupling dependence of two- and three-point functions of chiral primary fields in ${ m SU}(2)$ ${ m N}=2$ SCQCD. By combining four-dimensional ${tt}^*$-like relations with supersymmetric localization on $S^4$, the authors derive a semi-infinite Toda-chain for the chiral-ring data $g_{2n}$, with $g_2$ fixed by the exact sphere partition function $Z_{S^4}$. Higher $g_{2n}$ and the corresponding three-point coefficients follow recursively, and all extremal correlators are determined from this data. Weak-coupling and instanton expansions are explicitly presented and checked against perturbative calculations up to two loops, illustrating that ${ m N}=2$ theories with marginal deformations admit exact, non-perturbative control of chiral-ring observables; a companion paper extends the framework to ${ m SU}(N)$ and elaborates technical details.

Abstract

We report an exact solution of 2- and 3-point functions of chiral primary fields in SU(2) N=2 super-Yang-Mills theory coupled to four hypermultiplets. It is shown that these correlation functions are non-trivial functions of the gauge coupling, obeying differential equations which take the form of the semi-infinite Toda chain. We solve these equations recursively in terms of the Zamolodchikov metric that can be determined exactly from supersymmetric localization on the four-sphere. Our results are verified independently in perturbation theory with a Feynman diagram computation up to 2-loops. This is a short version of a companion paper that contains detailed technical remarks, additional material and aspects of an extension to SU(N) gauge group.