Noncommutativity and Model Building

TL;DR

This paper explores how noncommutative gauge theories can incorporate matter fields and embed supersymmetric models, showing that at high energies they resemble commutative theories, while at low energies they naturally break supersymmetry and decouple U(1) sectors.

Contribution

It introduces a method to include matter in noncommutative gauge theories and demonstrates embedding of supersymmetric models, with a concrete noncommutative GUT example.

Findings

Noncommutative U(N) theories can embed ordinary SU(N) models at high energies.

U(1) degrees of freedom decouple at low energies due to IR/UV mixing.

A noncommutative U(5) GUT model with supersymmetry breaking is constructed.

Abstract

We propose a way to introduce matter fields transforming in arbitrary representations of the gauge group in noncommutative U(N) gauge theories. We then argue that in the presence of supersymmetry, an ordinary commutative SU(N) gauge theory with a general matter content can always be embedded into a noncommutative U(N) theory at energies above the noncommutativity mass scale M_{NC} ~ \theta^{-1/2}. At energies below M_{NC}, the U(1) degrees of freedom decouple due to the IR/UV mixing, and the noncommutative theory reduces to its commutative counterpart. Supersymmetry can be spontaneously broken by a Fayet-Iliopoulos D-term introduced in the noncommutative U(N) theory. U(1) degrees of freedom become arbitrarily weakly coupled in the infrared and naturally play the role of the hidden sector for supersymmetry breaking. To illustrate these ideas we construct a noncommutative U(5) GUT model with Fayet-Iliopoulos supersymmetry breaking, which reduces to a realistic commutative theory in the infrared.