3 v 1 1 2 Se p 20 01 Spacetime as a Membrane in Higher Dimensions

By means of a simple model we investigate the possibility that spacetime is a membrane embedded in higher dimensions. We present cosmological solutions of d-dimensional Einstein-Maxwell theory which compactify to two dimensions. These solutions are analytically continued to obtain dual solutions in which a (d − 2)-dimensional Einstein spacetime " membrane " is embedded in d-dimensions. The membrane solutions generalise Melvin's 4-dimensional flux tube solution. The flat membrane is shown to be classically stable. It is shown that there are zero mode solutions of the d-dimensional Dirac equation which are confined to a neighbourhood of the membrane and move within it like mass-less chiral (d − 2)-dimensional fermions. An investigation of the spectrum of scalar perturbations shows that a well-defined mass gap between the zero modes and massive modes can be obtained if there is a positive cosmological term in (d − 2) dimensions or a negative cosmological term in d dimensions. [Note added 2001: In this early brane world model we sought to realise spacetime as a codimension two " thick brane " warped product submanifold of a higher–dimensional curved spacetime, as distinct from the previous models of K. 267 = hep-th/0001113] and Rubakov and Shaposhnikov [26], which involved field theoretic trappings of matter in a higher-dimensional flat spacetime, and Visser's model [9] in which the physical spacetime did not possess an exact Lorentz invariance.]