Exact Three-Point Functions in $\mathcal{N}=2$ Superconformal Field Theories: Integrability vs. Localization

We propose an integrability approach for planar three-point functions at finite coupling in $\mathcal{N}=2$ superconformal field theories obtained as $\mathbb{Z}_K$ orbifolds of $\mathcal{N}=4$ super Yang-Mills (SYM). Generalizing the hexagon formalism for $\mathcal{N}=4$ SYM, we reproduce the structure constants of Coulomb branch operators, previously obtained by supersymmetric localization, as exact functions of the 't Hooft coupling. Our analysis explains the common physical origin of Fredholm kernels in integrability and localization, and hints at structures after the resummation in the hexagon formalism.