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We consider the coupling of fermions to the three-dimensional noncommutative$CP^{N-1}$ model. In the case of minimal coupling, although the infraredbehavior of the gauge sector is improved, there are dangerous (quadratic)infrared divergences in the corrections to the two point vertex function of thescalar field. However, using superfield techniques we prove that thesupersymmetric version of this model with ``antisymmetrized'' coupling of theLagrange 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-Simonsnoncommutative terms in the effective action. Up to the 1/N order alldivergences are only logarithimic so that the model is free from nonintegrableinfrared singularities.Comment: Minor corrections in the text and modifications in the list of  reference

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Coupling of fermions to the three-dimensional noncommutative<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">CP</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mi>−</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>model: Minimal and supersymmetric extensions

Coupling of fermions to the three-dimensional noncommutativeCPN−1model: Minimal and supersymmetric extensions