1/2 BPS Wilson loops in non-conformal \( \mathcal{N} \) = 2 gauge theories and localization: a three-loop analysis

Abstract

We study the 1/2 BPS circular Wilson loop in four-dimensional SU(N) \( \mathcal{N} \) = 2 SYM theories with massless hypermultiplets and non-vanishing β-function. Using supersymmetric localization on 𝕊⁴, we map the path-integral associated with this observable onto an interacting matrix model. Despite the breaking of conformal symmetry at the quantum level, we show that, within a specific regime, the matrix model predictions remain consistent with the perturbative results in flat space up to order g⁶. At this order, our analysis reveals that the reorganization of Feynman diagrams based on the matrix model interaction potential, widely tested in (super)conformal models, also applies to these non-conformal set-ups and is realized by interference mechanisms.