Superbranes and superembeddings

We review a geometrical approach to the description of the dynamics of superparticles, superstrings and, in general, of super-p-branes, Dirichlet branes and the M5-brane, which is based on a generalization of the elements of surface theory to the description off the embedding of supersurfaces into target superspaces. Being manifestly supersymmetric in both, the superworldvolume of the brane and the target superspace, this approach unifies the Neveu-Schwarz-Ramond and the Green-Schwarz formulation and provides the fermionic re-symmetry of the Green-Schwarz-type superbrane actions with a clear geometrical meaning of standard worldvolume local supersymmetry. The dynamics of superbranes is encoded in a generic superembedding condition. Depending on the superbrane and the target-space dimension, the superembedding condition produces either only off-shell constraints las in the case of N = 1 superparticles and N = 1 superstrings), or also results in the full set of the superbrane equations of motion las, for example, in the case of the M-theory branes). In the first case worldvolume superspace actions for the superbranes can be constructed, while in the second case only component or generalized superfield actions are known. We describe the properties of the doubly supersymmetric brane actions and show how they are related to the standard Green-Schwarz formulation. In the second part of the article basic geometrical grounds of the (super)embedding approach are considered and applied to the description of the M2-brane and the M5-brane. Various applications of the superembedding approach are reviewed. (C) 2000 Elsevier Science B.V. All rights reserved.