Superbranes and Generic Curved Spacetime

TL;DR

This paper investigates the embedding of superbranes into curved spacetimes, revealing restrictions on curving and proposing extensions to accommodate generic curvings via advanced spinorial representations.

Contribution

It introduces a method to embed superbranes into generic curved spacetimes by extending the odd sector to infinite-component spinorial representations, overcoming previous limitations.

Findings

Superbranes can be embedded into restricted curved spacetimes.

Extending the odd sector allows for generic curving embedding.

Constructs are exemplified in D=3 dimensions.

Abstract

Embedding of a bosonic and/or fermionic p-brane into a generic curved $D$-dimensional spacetime is considered. In contradistinction to the bosonic p-brane case, when there are no constraints on a generic curving whatsoever, the usual superbrane can be embedded into a curved spacetime of a restricted curving only. A generic curving is achieved by extending the odd sector of a superbrane as to transform w.r.t. $\bar{SL}(D,R)$, i.e. $\bar{Diff}(D,R)$ infinite-component spinorial representations. Relevant constructions in the D=3 case are considered.