Vacua of M-theory and N=2 strings

String and membrane dynamics may be unified into a theory of (2 + 2)-dimensional self-dual world-volumes living in a (10 + 2)-dimensional target space. Some of the vacua of this M-theory are described by the N = (2, 1) heterotic string, whose target space theory describes the world-volume dynamics of (2 + 2)-dimensional 'M-branes'. All classes of string and membrane theories are realized as particular vacua of the N = (2, 1) string: Type IIA/B strings and supermembranes arise in the standard moduli space of toroidal compactifications, while type I' and heterotic strings arise from a Z(2) orbifold of the N = 2 algebra. Yet another vacuum describes M-theory on a T-5/Z(2) orientifold, the type I string on T-4, and the six-dimensional self-dual string, We find that open membranes carry 'Chan-Paton fields' on their boundaries, providing a common origin for gauge symmetries in M-theory. The world-volume interactions of M-brane fluctuations agree with those of Born-Infeld effective dynamics of the Dirichlet two-brane in the presence of a non-vanishing electromagnetic field on the brane.