The coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model: minimal and supersymmetric extensions

Details The coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model: minimal and supersymmetric extensions The coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model: minimal and supersymmetric extensions

2004-02-02

arxiv.org/abs/hep-th/0402013v2

Phys.Rev. D69 (2004) 105012

Physics

High Energy Physics

High Energy Physics - Theory

Minor corrections in the text and modifications in the list of references

Scientific paper

10.1103/PhysRevD.69.105012

We consider the coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model. In the case of minimal coupling, although the infrared behavior of the gauge sector is improved, there are dangerous (quadratic) infrared divergences in the corrections to the two point vertex function of the scalar field. However, using superfield techniques we prove that the supersymmetric version of this model with ``antisymmetrized'' coupling of the Lagrange multiplier field is renormalizable up to the first order in $\frac{1}{N}$. The auxiliary spinor gauge field acquires a nontrivial (nonlocal) dynamics with a generation of Maxwell and Chern-Simons noncommutative terms in the effective action. Up to the 1/N order all divergences are only logarithimic so that the model is free from nonintegrable infrared singularities.

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