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

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.

1+26 pages, figures using axodraw, clarifications added

References in corpus (15)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Construction of non-Abelian gauge theories on noncommutative spaces
• Non(anti)commutative Superspace
• Noncommutative Standard Model: Model Building
• Renormalization of noncommutative U(N) gauge theories
• Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups
• Exact Results in Noncommutative $\mathcal{N}=2$ Supersymmetric Gauge Theories
• Noncommutative o*(N) and usp*(2N) algebras and the corresponding gauge field theories
• The Three-Dimensional Noncommutative Nonlinear Sigma Model in Superspace
• On non-commutative N=2 super Yang-Mills
• Superfield Effective Action in the Noncommutative Wess-Zumino Model
• The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level
• On Low-Energy Effective Action of Noncommutative Hypermultiplet Model
• Noncommutative N=2 Supersymmetric Theories in Harmonic Superspace

Cited by in corpus (4)

• On Matrix Model Formulations of Noncommutative Yang-Mills Theories
• Renormalization of the energy-momentum tensor in noncommutative scalar field theory
• Renormalization of the energy-momentum tensor in noncommutative complex scalar field theory
• One-loop Renormalized Coefficient of Noncommutative Supersymmetric Yang-Mills-Chern-Simons Gauge Theories in Three Dimensions