Aspects of model building in noncommutaive quantum field theories

Abstract

We review quantum field theories on noncommutative Minkowski spaces (NCQFTs), concentrating on the mixing between ultra-violet and infra-red degrees of freedom in such theories. We use background field perturbation theory at the one-loop level to calculate the three and four point functions in supersymmetric NCQFT. We use the results of this calculation to show that the infra-red logarithmic divergences that arise as a result of the UV/IR mixing can be reproduced by an explicitly gauge-invariant low-energy effective action expressed in terms of Wilson lines. 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 satisfies all the key constraints that are 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 decouple due to the UV/IR mixing. Our model also predicts the values of the hypercharges of the Standard Model fields. We find that in order to accomodate the matter content of the Standard Model it is necessary to introduce extra, as yet undetected, matter fields. [brace not closed]