Remarks on BPS Wilson loops in non-conformal $$ \mathcal{N} $$ = 2 gauge theories and localization

A bstract We consider 1/2 BPS supersymmetric circular Wilson loops in four-dimensional $$ \mathcal{N} $$ N = 2 SU( N ) SYM theories with massless matter content and non-vanishing β -function. Following Pestun’s approach, we can use supersymmetric localization on the sphere $$ \mathbbm{S} $$ S 4 to m...

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Published in:The journal of high energy physics 2024-01, Vol.2024 (1), Article 160
Main Authors: Billò, M., Griguolo, L., Testa, A.
Format: Article
Language:English
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Summary:A bstract We consider 1/2 BPS supersymmetric circular Wilson loops in four-dimensional $$ \mathcal{N} $$ N = 2 SU( N ) SYM theories with massless matter content and non-vanishing β -function. Following Pestun’s approach, we can use supersymmetric localization on the sphere $$ \mathbbm{S} $$ S 4 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 $$ \mathbbm{S} $$ S 4 . 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 β -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 .
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP01(2024)160