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Renormalizing Yukawa interactions in the standard model with matrices and noncommutative geometry

We show that gauge-independent terms in the one-loop and multi-loops $β$-functions of the Standard Model can be exactly computed from the Wetterich functional renormalization of a matrix model. Our framework is associated to the finite spectral triple underlying the computation of the Standard Model Lagrangian from the spectral action of Noncommutative Geometry. This matrix-Yukawa duality for the $β$-function is a first hint towards understanding the renormalization of the Noncommutative Standard Model conceptually, and provides a novel computational approach for multi-loop $β$-functions of particle physics models.