Superembedding Approach to Superstrings and Super-p-branes

We review a geometrical, so-called superembedding, approach to the description of the dynamics of point-like and extended supersymmetric objects (superbranes) in string theory. The approach is based on a supersymmetric extension of the classical surface theory to the description of superbrane dynamics by means of embedding worldvolume supersurfaces into target superspacesTarget superspace. Lorentz harmonics, twistors, and pure spinors are its intrinsic ingredients. The main new results obtained with this approach include the following ones. Being manifestly doubly supersymmetric (on the worldvolume and in target superspaceTarget superspace), the superembedding approach explained that the local fermionic kappa-symmetry of the Green-Schwarz-like superbrane actions originates from the conventional local supersymmetry of the worldvolume. It established or clarified a classical relationship between various formulations of the dynamics of superparticles and superstrings, such as the Neveu-Schwarz-Ramond and the Green-Schwarz formulation. The full set of the equations of motion of the M-theory five-brane was first derived with the use of this approach.