Superembeddings, Non-Linear Supersymmetry and 5-branes

TL;DR

This paper explores superembeddings and their relation to non-linear supersymmetry, illustrating the concepts through the example of a super-5-brane in 7 dimensions with a self-dual 3-form field.

Contribution

It clarifies the connection between superembeddings and non-linear supersymmetry and demonstrates their application to a super-5-brane model.

Findings

Superembeddings encompass non-linear supersymmetry as a special case.

The super-5-brane in 7D with a self-dual 3-form is formulated using both approaches.

Embedding conditions may not always suffice to put the theory on-shell.

Abstract

We examine general properties of superembeddings, i.e., embeddings of supermanifolds into supermanifolds. The connection between an embedding procedure and the method of non-linearly realised supersymmetry is clarified, and we demonstrate how the latter arises as a special case of the former. As an illustration, the super-5-brane in 7 dimensions, containing a self-dual 3-form world-volume field strength, is formulated in both languages, and provides an example of a model where the embedding condition does not suffice to put the theory on-shell.