Non-Linear Sigma Model on the Fuzzy Supersphere

TL;DR

This paper constructs a fuzzy supersymmetric non-linear sigma model on the supersphere S^(2,2) using supersymmetric projectors, leading to a finite-dimensional matrix model that extends previous fuzzy CP^1 models.

Contribution

It introduces a novel fuzzy supersymmetric sigma model on the supersphere by extending supersymmetric projectors, providing a new approach to quantization in this context.

Findings

Developed supersymmetric projectors for the fuzzy supersphere

Quantized the projectors to form a finite matrix model

Provided interpretation of the model as a finite-dimensional matrix system

Abstract

In this note we develop fuzzy versions of the supersymmetric non-linear sigma model on the supersphere S^(2,2). In hep-th/0212133 Bott projectors have been used to obtain the fuzzy CP^1 model. Our approach utilizes the use of supersymmetric extensions of these projectors. Here we obtain these (super) -projectors and quantize them in a fashion similar to the one given in hep-th/0212133. We discuss the interpretation of the resulting model as a finite dimensional matrix model.