  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 massless 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.
