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

TL;DR

This paper investigates a noncommutative supersymmetric $CP^{(N-1)}$ model in 2+1 dimensions with fundamental representation fields, analyzing its phase structure, renormalizability, and quantum corrections.

Contribution

It introduces the fundamental representation version of the noncommutative supersymmetric $CP^{(N-1)}$ model and demonstrates its renormalizability and absence of UV/IR singularities.

Findings

Model is free of non-integrable UV/IR singularities

Proven renormalizability at leading order

Calculated and renormalized two-point function up to subleading order

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 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.