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

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

2006-12-20

arxiv.org/abs/hep-th/0612223v3

J.Phys.A40:7803-7818,2007

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/1751-8113/40/27/024

In this paper we study the noncommutative supersymmetric $CP^{(N-1)}$ 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 $CP^{(N-1)}$ 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.

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