Correlators in non-conformal $\mathcal{N}=2$ gauge theories from localization

TL;DR

This paper demonstrates that supersymmetric localization accurately computes two-point functions in non-conformal $ ext{SU}(N)$ $ ext{N}=2$ gauge theories, matching perturbative Feynman diagram results up to two loops and revealing the importance of interference effects.

Contribution

It extends the comparison between localization and perturbative calculations to non-conformal $ ext{N}=2$ theories with general matter representations, highlighting the role of evanescent terms and UV poles.

Findings

Localization results match two-loop perturbative calculations.

Interference effects between evanescent terms and UV poles are crucial.

Matrix model diagrammatic approach simplifies comparisons.

Abstract

We study two-point correlation functions of chiral/anti-chiral operators in SU(N) $\mathcal{N}=2$ gauge theories with massless hyper-multiplets in a representation $\mathcal{R}$ associated with a non-vanishing $\beta$-function. Using supersymmetric localization on the four-sphere $S^4$, these observables can be evaluated by matrix correlators of normal ordered operators. We show that, within a specific regime of validity, standard perturbative calculations based on Feynman diagrams and renormalization procedures in flat space perfectly match the localization predictions up to two loops generalizing and extending previous results. Our analysis highlights that non-trivial interference effects between evanescent terms and the UV poles of the bare coupling are essential for the agreement. On the matrix model side, we employ a direct diagrammatic procedure akin to the Feynman diagram expansion on the field theory description; this simplifies the comparison for generic operators and general matter representation $\mathcal{R}$.