One-loop renormalization of general noncommutative Yang-Mills field model coupled to scalar and spinor fields

TL;DR

This paper demonstrates that a noncommutative U(N) Yang-Mills theory coupled with scalar and spinor matter fields is one-loop renormalizable, with all divergences absorbable through field and coupling constant redefinitions.

Contribution

It provides the first comprehensive one-loop renormalization analysis of a noncommutative Yang-Mills theory with diverse matter interactions, including previously unconsidered terms.

Findings

All divergences are absorbed by renormalization of fields and couplings.

The theory is multiplicatively renormalizable at one loop.

Results can be extended to multiple matter fields with appropriate coupling adjustments.

Abstract

We study the theory of noncommutative U(N) Yang-Mills field interacting with scalar and spinor fields in the fundamental and the adjoint representations. We include in the action both the terms describing interaction between the gauge and the matter fields and the terms which describe interaction among the matter fields only. Some of these interaction terms have not been considered previously in the context of noncommutative field theory. We find all counterterms for the theory to be finite in the one-loop approximation. It is shown that these counterterms allow to absorb all the divergencies by renormalization of the fields and the coupling constants, so the theory turns out to be multiplicatively renormalizable. In case of 1PI gauge field functions the result may easily be generalized on an arbitrary number of the matter fields. To generalize the results for the other 1PI functions it is necessary for the matter coupling constants to be adapted in the proper way. In some simple cases this generalization for a part of these 1PI functions is considered.