Superbranes

TL;DR

Howe and Sezgin develop a geometrical, embedding-based framework for super p-branes that replaces κ-symmetry with local worldvolume supersymmetry. The core tool is the master embedding constraint, whose linearised form $D_\alpha \tilde{X}^{a'} = i(\Gamma^{a'})_{\alpha\beta'} \Theta^{\beta'}$ connects worldvolume superfields to target-space structures and determines the resulting worldvolume multiplets. Application to the $D=11$ superfivebrane yields an on-shell $d=6,N=(2,0)$ tensor multiplet with a self-dual 3-form, while a systematic scan classifies Type I/II branes and introduces L-branes, mapping each to specific multiplets (on-shell or off-shell). The approach offers a path to nonlinear dynamics, clarifies the role of DBI-type structures in Type II branes, and frames branes as potential solitons of supergravity with avenues for studying intersections and reduced supersymmetry.

Abstract

A large class of supersymmetric extended objects is considered from the viewpoint of embeddings of super worldsurfaces into target superspaces. It is shown that a simple geometrical condition leads to the equations of motion for the brane in many cases.