The supersymmetric (2 + 1)D noncommutative CP(N−1) model in the fundamental representation

Abstract

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 analyse 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.