Noncommutative Standard Modelling

TL;DR

This paper introduces a noncommutative gauge theory model that reproduces the Standard Model at low energies, addressing noncommutative constraints and predicting hypercharge values.

Contribution

It constructs a noncommutative gauge theory based on U(4) x U(3) x U(2) that satisfies key noncommutative requirements and recovers the Standard Model in the low-energy limit.

Findings

Model reproduces Standard Model at low energies

Predicts hypercharge values for Standard Model fields

Addresses noncommutative constraints like UV/IR mixing

Abstract

We present a noncommutative gauge theory that has the ordinary Standard Model as its low-energy limit. The model is based on the gauge group U(4) x U(3) x U(2) and is constructed to satisfy the key requirements imposed by noncommutativity: the UV/IR mixing effects, restrictions on representations and charges of matter fields, and the cancellation of noncommutative gauge anomalies. At energies well below the noncommutative mass scale our model flows to the commutative Standard Model plus additional free U(1) degrees of freedom which are decoupled due to the UV/IR mixing. Our model also predicts the values of the hypercharges of the Standard Model fields.