New Principles for String/Membrane Unification

Abstract

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.