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 considered. We show 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. ”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 KalbRamond background and its relation to a first order Einstein-Cartan approach for d = 2 dimensional gravity is analysed in some detail. A general Poisson-sigma-model structure emerges. For the minimal choice of D = 3 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). PACs: 11.15-q, 11.17+y, 04.60.Kz, 04.50.+h, 11.10.Kk.11.30-j.