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There have been various proposals for models of "Gravity a la string" in the style of Regge-Teitelboim.
Here I shall propose a background field approach based on an embedding of spacetime into 14 dimensional Minkowski space. The importance of free embeddings, in which the second fundamental form is nodegenerate in a certain sense, is emphasised. In this context, the linearised theory is seen to be equivalent to GR. The full nonlinear theory is more compllicated. Preliminary results regarding the initial value formulation will be discussed.