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

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