ITP – UH – 09 / 96 June 1996 hep - th / 9606142 From N = 2 Strings to F & M Theory

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 the F & M theory. Supported in part by the ‘Deutsche Forschungsgemeinschaft’ and the ‘Volkswagen Stiftung’ Talk given at the International Workshop ‘Integrable Models and Strings, 24–25 June, 1996, Garbsen, Germany 3 On leave of absence from: High Current Electronics Institute of the Russian Academy of Sciences, Siberian Branch, Akademichesky 4, Tomsk 634055, Russia