The coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model: minimal and supersymmetric extensions

TL;DR

This paper investigates the coupling of fermions to a three-dimensional noncommutative $CP^{N-1}$ model, demonstrating that supersymmetric extensions are renormalizable and free from severe infrared divergences at the first order in 1/N.

Contribution

It introduces a supersymmetric version of the noncommutative $CP^{N-1}$ model with antisymmetrized coupling, proving its renormalizability and analyzing the effective gauge dynamics.

Findings

Supersymmetric model is renormalizable up to 1/N order.

Auxiliary gauge field acquires nonlocal Maxwell and Chern-Simons terms.

Model remains free from nonintegrable infrared divergences at this order.

Abstract

We consider the coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model. In the case of minimal coupling, although the infrared behavior of the gauge sector is improved, there are dangerous (quadratic) infrared divergences in the corrections to the two point vertex function of the scalar field. However, using superfield techniques we prove that the supersymmetric version of this model with ``antisymmetrized'' coupling of the Lagrange multiplier field is renormalizable up to the first order in $\frac{1}{N}$. The auxiliary spinor gauge field acquires a nontrivial (nonlocal) dynamics with a generation of Maxwell and Chern-Simons noncommutative terms in the effective action. Up to the 1/N order all divergences are only logarithimic so that the model is free from nonintegrable infrared singularities.