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

Abstract

We investigate possible extensions of the (2+1) dimensional $C{P}^{N-1}$ 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 $\varphi$ 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 $\varphi$ 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.

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

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Cited by in corpus (5)

• The Supersymmetric (2+1)D Noncommutative $C{P}^{(N-1)}$ Model in the Fundamental Representation
• The coupling of fermions to the three-dimensional noncommutative $C{P}^{N-1}$ model: minimal and supersymmetric extensions
• $C{P}^{(N-1)}$ model in aether-superspace
• The Slavnov-Taylor Identities for the 2+1 Dimensional Noncommutative CP${}^{N-1}$ Model
• The 1/N Expansion in Noncommutative Quantum Mechanics