(2+1)D Noncommutative CP$^{N-1}$ Model

Details (2+1)D Noncommutative CP$^{N-1}$ Model (2+1)D Noncommutative CP$^{N-1}$ Model

2003-07-11

arxiv.org/abs/hep-th/0307114v3

Phys.Rev. D69 (2004) 065012

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, 11 figures, revtex4, minor corrections in some equations and in the text

Scientific paper

10.1103/PhysRevD.69.065012

We investigate possible extensions of the (2+1) dimensional $CP^{N-1}$ model to the 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 $\phi$ transforms in accord with the adjoint representation, infrared singularities are present in the two point function of the auxiliary gauge field and also in the leading correction to the self-energy of the $\phi$ 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.

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