Superbranes, D=11 CJS supergravity and enlarged superspace coordinates/fields correspondence

TL;DR

This paper explores how enlarged superspaces unify the description of p-branes and D=11 supergravity, revealing that all fields can be viewed as coordinates in these extended superspaces, with a common algebraic and cohomological framework.

Contribution

It demonstrates the role of enlarged superspaces in expressing all worldvolume and spacetime fields as coordinates, unifying p-brane actions and supergravity through algebraic structures.

Findings

Enlarged superspaces enable manifestly supersymmetric Wess-Zumino terms.

Born-Infeld and other worldvolume fields have a superspace origin.

A family of superspace groups describes the composite nature of the A_3 field in D=11 supergravity.

Abstract

We discuss the r\^ole of enlarged superspaces in two seemingly different contexts, the structure of the $p$-brane actions and that of the Cremmer-Julia-Scherk eleven-dimensional supergravity. Both provide examples of a common principle: the existence of an {\it enlarged superspaces coordinates/fields correspondence} by which all the (worldvolume or spacetime) fields of the theory are associated to coordinates of enlarged superspaces. In the context of $p$-branes, enlarged superspaces may be used to construct manifestly supersymmetry-invariant Wess-Zumino terms and as a way of expressing the Born-Infeld worldvolume fields of D-branes and the worldvolume M5-brane two-form in terms of fields associated to the coordinates of these enlarged superspaces. This is tantamount to saying that the Born-Infeld fields have a superspace origin, as do the other worldvolume fields, and that they have a composite structure. In $D$=11 supergravity theory enlarged superspaces arise when its underlying gauge structure is investigated and, as a result, the composite nature of the $A_3$ field is revealed: there is a full one-parametric family of enlarged superspace groups that solve the problem of expressing $A_3$ in terms of spacetime fields associated to their coordinates. The corresponding enlarged supersymmetry algebras turn out to be deformations of an {\it expansion} of the $osp(1|32)$ algebra. The unifying mathematical structure underlying all these facts is the cohomology of the supersymmetry algebras involved.