The geometry of branes and extended superspaces

TL;DR

This paper develops a unified geometric framework enlarging superspace to include extended objects like p-branes, enabling manifestly supersymmetric actions and clarifying the origin of central charges in superalgebras.

Contribution

It introduces an enlarged superspace approach that systematically derives superalgebras and constructs supersymmetric actions for various p-branes, including D-branes with Born-Infeld fields.

Findings

Recovered generalized superalgebras and extensions of supersymmetry.

Constructed manifestly supersymmetric p-brane actions.

Clarified the origin of central charges in superalgebras.

Abstract

We argue that a description of supersymmetric extended objects from a unified geometric point of view requires an enlargement of superspace. To this aim we study in a systematic way how superspace groups and algebras arise from Grassmann spinors when these are assumed to be the only primary entities. In the process, we recover generalized spacetime superalgebras and extensions of supersymmetry found earlier. The enlargement of ordinary superspace with new parameters gives rise to extended superspace groups, on which manifestly supersymmetric actions may be constructed for various types of p-branes, including D-branes (given by Chevalley-Eilenberg cocycles) with their Born-Infeld fields. This results in a field/extended superspace democracy for superbranes: all brane fields appear as pull-backs from a suitable target superspace. Our approach also clarifies some facts concerning the origin of the central charges for the different p-branes.