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

Abstract

We show that gauge-independent terms in the one-loop and multi-loops $\beta$-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 $\beta$-function is a first hint towards understanding the renormalization of the Noncommutative Standard Model conceptually, and provides a novel computational approach for multi-loop $\beta$-functions of particle physics models.

arXiv comment19 pages, 4 figures v2: minor corrections, enhanced presentation and discussion

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Cited by in corpus (4)

• Bootstrapping Dirac Ensembles
• Random Finite Noncommutative Geometries and Topological Recursion
• From Noncommutative Geometry to Random Matrix Theory
• One-loop corrections to the spectral action