New Principles for String/Membrane Unification

The target space theory of the N=(2,1) heterotic string may be interpreted as a theory of gravity coupled to matter in either 1 + 1 or 2 + 1 dimensions. Among the target space theories in 1+ 1 dimensions are the bosonic, type II, and heterotic string world sheet field theories in a physical gauge. The 2+1 dimensional version describes a consistent quantum theory of supermembranes in 10 + 1 dimensions. The unifying framework for all of these vacua is a theory of 2+2 dimensional self-dual geometries embedded in 10+2 dimensions. There are also indications that the N=(2,1) string describes the strong coupling dynamics of compactifications of critical string theories to two dimensions, and may lead to insights about the fundamental degrees of freedom of the theory.