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

## TL;DR

This paper introduces a novel approach to compute gauge-independent multi-loop beta functions in the Standard Model using a matrix model framework derived from noncommutative geometry, offering new insights into renormalization.

## Contribution

It establishes a matrix-Yukawa duality for beta functions and connects noncommutative geometry with renormalization in particle physics models.

## Key findings

- Exact computation of gauge-independent beta functions from matrix models.
- First demonstration of matrix-Yukawa duality in renormalization.
- Provides a new computational method for multi-loop beta functions.

## 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.