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

TL;DR

This paper investigates the behavior of 1/2 BPS Wilson loops in non-conformal N=2 gauge theories using localization, showing consistency with perturbative results up to three loops despite broken conformal symmetry.

Contribution

It demonstrates that matrix model predictions for Wilson loops remain valid in non-conformal N=2 theories up to order g^6, extending methods from conformal models.

Findings

Matrix model predictions align with perturbative calculations up to three loops.

Reorganization of Feynman diagrams applies to non-conformal theories.

Interference mechanisms realize matrix model interactions in non-conformal setups.

Abstract

We study the 1/2 BPS circular Wilson loop in four-dimensional SU(N), $N = 2$ SYM theories with massless hypermultiplets and non-vanishing $\beta$-function. Using super-symmetric 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.