Abstract
We consider 1/2 BPS supersymmetric circular Wilson loops in four-dimensional \( \mathcal{N} \) = 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 \( \mathbbm{S} \)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 g4, the predictions for the 1/2 BPS Wilson loop match standard perturbative renormalization based on the direct evaluation of Feynman diagrams on \( \mathbbm{S} \)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 g6.
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Acknowledgments
We would like to thank M. Frau, F. Galvagno, R. R. John, A. Lerda, A. Miscioscia, I. Pesando and D. Seminara for many useful discussions. This research is partially supported by the MIUR PRIN contract 2020KR4KN2 “String Theory as a bridge between Gauge Theories and Quantum Gravity” and by the INFN projects ST&FI “String Theory & Fundamental Interactions” and GAST “Gauge Theory And Strings”.
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Billò, M., Griguolo, L. & Testa, A. Remarks on BPS Wilson loops in non-conformal \( \mathcal{N} \) = 2 gauge theories and localization. J. High Energ. Phys. 2024, 160 (2024). https://doi.org/10.1007/JHEP01(2024)160
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DOI: https://doi.org/10.1007/JHEP01(2024)160