The Supersymmetric (2+1)D Noncommutative $C{P}^{(N-1)}$ Model in the Fundamental Representation

Abstract

In this paper we study the noncommutative supersymmetric $C{P}^{(N-1)}$ model in 2+1 dimensions, where the basic field is in the fundamental representation which, differently to the adjoint representation already studied in the literature, goes to the usual supersymmetric $C{P}^{(N-1)}$ model in the commutative limit. We analyze the phase structure of the model and calculate the leading and subleading corrections in a 1/N expansion. We prove that the theory is free of non-integrable UV/IR infrared singularities and is renormalizable in the leading order. The two-point vertex function of the basic field is also calculated and renormalized in an explicitly supersymmetric way up to the subleading order.

arXiv comment20 pages, 6 figures, revtex4; v3, final version to be published in J. Phys.A

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• Supersymmetry breaking in the three-dimensional nonlinear sigma model
• Dynamical generation of mass in the noncommutative supersymmetric Schwinger model
• Soft supersymmetry breaking in the nonlinear sigma model
• Perturbative aspects of the supersymmetric three-dimensional massive QED