From N=2 strings to F&M theory

Abstract

Taking the N=2 strings as the starting point, we discuss the equivalent self-dual field theories and analyse their symmetry structure in 2+2 dimensions. Restoring the full `Lorentz' invariance in the target space necessarily leads to an extension of the N=2 string theory to a theory of 2+2 dimensional supermembranes propagating in 2+10 dimensional target space. The supermembrane requires maximal conformal supersymmetry in 2+2 dimensions, in the way advocated by Siegel. The corresponding self-dual N=4 Yang-Mills theory and the self-dual N=8 (gauged) supergravity in 2+2 dimensions thus appear to be naturally associated to the membrane theory, not a string. Since the same theory of membranes seems to represent the M-theory which is apparently underlying the all known N=1 string theories, the N=2 strings now appear on equal footing with the other string models as particular limits of the unique fundamental theory. Unlike the standard 10-dimensional superstrings, the N=2 strings seem to be much closer to a membrane description of F&M theory.