Abstract
Taking the (2, 2) strings as a starting point, we discuss the equivalent integrable field theories and analyze their symmetry structure in 2+2 dimensions from the viewpoint of string/membrane unification. Requiring the “Lorentz” invariance and supersymmetry in the (2, 2) string target space leads to an extension of the (2, 2) string theory to a theory of (2+2)-dimensional supermembranes (M-branes) propagating in a higher-dimensional target space. The origin of the hidden target space dimensions of the M-brane is related to the maximally extended supersymmetry implied by the “Lorentz” covariance and dimensional reasons. The Kähler-Chern-Simons-type action describing the self-dual gravity in 2+2 dimensions is proposed. Its maximal supersymmetric extension (of the Green-Schwarz-type) naturally leads to the 2+10 (or higher) dimensions for the M-brane target space. The proposed OSp (32|1) supersymmetric action gives the pre-geometrical description of M-branes, which may be useful for a fundamental formulation of F&M theory.
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