The geometry of branes and extended superspaces

TL;DR

The paper develops a unified, geometric framework in which all supersymmetric branes arise from an enlargement of superspace initiated from Grassmann spinors. By classifying central and non-central extensions via Chevalley–Eilenberg cocycles and free differential algebras, it constructs extended superspace groups on which manifestly invariant brane actions can be defined, including D-branes whose worldvolume fields emerge as pullbacks from the extended target space. This leads to a field/extended superspace democracy in which the Wess–Zumino terms and Noether charges are naturally realized in the extended setting, clarifying the origin of central charges and their relation to brane dynamics. The approach provides concrete manifestly invariant formulations for the Green–Schwarz string, M2/M5-branes, and D-branes, and suggests a unified language for dualities and quantization in M-theory.

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.