On the generalized action principle for superstrings and supermembranes

We revise the twistor-like superfield approach to describing super-p-branes by use of the basic principles of the group-manifold approach [Y. Neʹeman and T. Regge, Phys. Lett. B 74 (1978) 54; Rivista del Nuovo Cim. 1 (1978) 1; R. DʹAuria, P. Frè and T. Regge, Rivista del Nuovo Cim. 3 1980 1; L. Castellani, R. DʹAuria and P. Frè, Supergravity and superstrings, a geometric perspective, World Scientific, Singapore, 1991 (and references therein)]. A super-p-brane action is constructed solely by geometrical objects as the integral over a (p + 1)-surface. The Lagrangian is the external product of supervielbein differential forms in world supersurface and target superspace without any use of Lagrange multipliers. This allows one to escape the problem of infinite reducible symmetries and redundant propagating fields. All the constraints on the geometry of world supersurface and the conditions of its embedding into target superspace arise from the action as differential form equations.