Strong and electroweak interactions and their unification with non-commutative space-time

Abstract

Quantum field theories based on noncommutative space-time (NCQFT) have been extensively studied recently. However no NCQFT model, which can uniquely describe the strong and electroweak interactions, has been constructed. This prevents consistent and systematic study of noncommutative space-time. In this work we construct a NCQFT model based on the trinification gauge group $SU(3)_C\times SU(3)_L\times SU(3)_R$. A unique feature of this model, that all matter fields (fermions and Higgses) are assigned to (anti-)fundamental representations of the factor SU(3) groups, allows us to construct a NCQFT model for strong and electroweak interactions and their unification without ambiguities. This model provides an example which allows consistent and systematic study of noncommutative space-time phenomenology. We also comment on some related issues regarding extensions to $E_6$ and $U(3)_C\times U(3)_L\times U(3)_R$ models.