p-branes, Poisson-sigma models and embedding approach to (p+1)-dimensional gravity

A generalization of the embedding approach for d-dimensional gravity based upon p-brane theories is proposed. We prove that the D-dimensional p-brane coupled to an antisymmetric tensor field of rank (p + 1) provides the dynamical basis for the description of d = (p + 1)-dimensional gravity in the isometric embedding formalism. By that we mean that the equations of motion following from this action describe any (p + 1)-dimensional space-time (at least locally) once the antisymmetric tensor field is chosen appropriately. "Physical" matter appears in such an approach as a manifestation of a D-dimensional antisymmetric tensor (generalized Kalb-Ramond) background. For the simplest case, the Lorentz harmonic formulation of the bosonic string in a Kalb-Ramond background and its relation to a first order Einstein-Cartan approach for (d = 2)-dimensional gravity is analyzed in some detail. We show that a general Poisson-sigma model structure emerges in this case. For the minimal choice of a free D = 3 string an interesting "dual" formulation is found which has the structure of a Jackiw-Teitelboim theory, coupled minimally to a massive scalar field. Our approach is intended to serve as a preparation for the study of d-dimensional supergravity theory, either starting from the generalized action of free supersymmetric (d - 1)-branes or D(d-1)-branes, or from the corresponding geometric equations ("rheotropic" conditions).