Speaker
Description
We consider 1/2 BPS supersymmetric circular Wilson loops in $\mathcal{N}=2$ $SU(N)$ SYM theories with massless matter content and non-vanishing $\beta$-function. In flat space we compute the observable via perturbative techniques, employing dimensional reduction to regularize the ultraviolet divergences and performing standard renormalization. We extend the analysis on the sphere $\mathbb{S}^4$ using both Feyman diagrams and the matrix model resulting from the localization procedure. On the matrix model side, working with a non-vanishing $\beta$-function requires a consistent regularization scheme to obtain a well-defined partition function. We show that at order $g^4$ a suitable procedure gives perfect agreement between localization predictions and standard perturbative renormalization. The results on $\mathbb{S}^4$ and those in flat space coincide for the Wilson loop at order $g^4$ even if conformal symmetry is broken at the quantum level, but we expect a mismatch at order $g^6$ due to an anomalous contribution which is generated by the renormalization procedure on the sphere and does not appear in $\mathbb{R}^4$.
