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

A bstract We study the 1/2 BPS circular Wilson loop in four-dimensional SU( N ) $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 SYM theories with massless hypermultiplets and non-vanishing β -function. Using supersymmetric localization on 𝕊 4 , 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 g 6 . 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.