Remarks on BPS Wilson loops in non-conformal N=2 gauge theories and localization

TL;DR

This paper investigates 1/2 BPS Wilson loops in non-conformal N=2 SU(N) theories, demonstrating that a regularized matrix model accurately predicts their behavior at perturbative order g^4, despite broken conformal symmetry.

Contribution

It constructs a consistent regularized matrix model for non-conformal N=2 theories and shows its predictions align with perturbative calculations at order g^4.

Findings

Matrix model reproduces perturbative results at order g^4

Broken conformal symmetry does not affect matrix model predictions at this order

Evanescent terms are crucial at order g^6 and are not captured by the difference theory approach

Abstract

We consider 1/2 BPS supersymmetric circular Wilson loops in four-dimensional N=2 SU(N) SYM theories with massless matter content and non-vanishing beta-function. Following Pestun's approach, we can use supersymmetric localization on the sphere S4 to map these observables into a matrix model, provided that the one-loop determinants are consistently regularized. Employing a suitable procedure, we construct the regularized matrix model for these theories and show that, at order g^4, the predictions for the 1/2 BPS Wilson loop match standard perturbative renormalization based on the direct evaluation of Feynman diagrams on S4. Despite conformal symmetry begin broken at the quantum level, we also demonstrate that the matrix model approaches perfectly captures the expression of the renormalized observable in flat space at this perturbative order. Moreover, we revisit in detail the difference theory approach, showing that when the beta-function is non-vanishing, this method does not account for evanescent terms which are made finite by the renormalization procedure and participate to the corrections at order g^6.