Non-Commutative GUTs, Standard Model and C,P,T

TL;DR

This paper investigates noncommutative grand unified theories, revealing that SO(10) admits a unique noncommutative extension and examining the properties of the Seiberg-Witten map in these models.

Contribution

It demonstrates that SO(10) GUTs have a unique noncommutative generalization and analyzes the properties of the Seiberg-Witten map in GUT-compatible models.

Findings

SU(5) is not a true noncommutative GUT at first order in θ.

SO(10) has a unique noncommutative generalization.

No modifications to the SM gauge kinetic term at lowest order in θ.

Abstract

Noncommutative Yang-Mills theories are sensitive to the choice of the representation that enters in the gauge kinetic term. We constrain this ambiguity by considering grand unified theories. We find that at first order in the noncommutativity parameter \theta, SU(5) is not truly a unified theory, while SO(10) has a unique noncommutative generalization. In view of these results we discuss the noncommutative SM theory that is compatible with SO(10) GUT and find that there are no modifications to the SM gauge kinetic term at lowest order in \theta. We study in detail the reality, hermiticity and C,P,T properties of the Seiberg-Witten map and of the resulting effective actions expanded in ordinary fields. We find that in models of GUTs (or compatible with GUTs) right-handed fermions and left-handed ones appear with opposite Seiberg-Witten map.