(2+1)dimensional noncommutative CP^{N1} model
Abstract
We investigate possible extensions of the (2+1)dimensional CP^{N1} model to noncommutative space. Up to the leading nontrivial order of 1/N, we prove that the model restricted to the left fundamental representation of the gauge group is renormalizable and does not have dangerous infrared divergences. In contrast, if the basic field φ transforms in accord with the adjoint representation, infrared singularities are present in the twopoint function of the auxiliary gauge field and also in the leading correction to the selfenergy of the φ field. These infrared divergences may produce nonintegrable singularities leading at higher orders to a breakdown of the 1/N expansion. Gauge invariance of the renormalization procedure is also discussed.
 Publication:

Physical Review D
 Pub Date:
 March 2004
 DOI:
 10.1103/PhysRevD.69.065012
 arXiv:
 arXiv:hepth/0307114
 Bibcode:
 2004PhRvD..69f5012A
 Keywords:

 11.10.Nx;
 11.10.Gh;
 11.10.Lm;
 11.15.q;
 Noncommutative field theory;
 Renormalization;
 Nonlinear or nonlocal theories and models;
 Gauge field theories;
 High Energy Physics  Theory
 EPrint:
 31 pages, 11 figures, revtex4, minor corrections in some equations and in the text