The Supersymmetric Extension of the Faddeev model

TL;DR

This paper explores the supersymmetric extension of the Faddeev model in four dimensions, revealing that supersymmetrization requires additional bosonic terms and that certain extensions can support solitons with mass bounds.

Contribution

It demonstrates how to construct supersymmetric versions of the Faddeev model, analyzing their soliton solutions and mass bounds, which was not previously established.

Findings

Supersymmetrization requires extra bosonic terms.

Two construction methods lead to models with or without solitons.

A lower mass bound for solitons is derived from the central charge.

Abstract

We study the supersymmetric extension of the Faddeev model in four dimensions. The Faddeev model contains three dimensional soliton solutions and we are interested in how these solitons are affected by supersymmetry. We consider both the N=1 and N=2 extensions and find that in neither case it is possible to supersymmetrize the model without adding additional bosonic terms. There are essentially two ways of constructing the supersymmetric theory, one that will lead to a model which allows for solitons and another that gives a model where solitons are excluded. The N=2 model is studied since extending supersymmetry is the natural way of including topological charges in the algebra. A lower bound to the mass is obtained by computing the central charge. The result is that it is possible to have a non-trivial lower bound on the mass, this in principle allows for massive solitons.