Membrane Vacuum as a Type II Superconductor

We study a functional field theory of membranes coupled to a rank--three tensor gauge potential. We show that gauge field radiative corrections lead to membrane condensation which turns the gauge field into a {\it massive spin--0 field}. This is the Coleman--Weinberg mechanism for {\it membranes}. An analogy is also drawn with a type--II superconductor. The ground state of the system consists of a two--phase medium in which the superconducting background condensate is ``pierced'' by four dimensional domains, or ``bags'', of non superconducting vacuum. Bags are bounded by membranes whose physical thickness is of the order of the inverse mass acquired by the gauge field.