Space-Time Supersymmetry of Extended Fermionic Strings in $2+2$ Dimensions

Abstract

The $N=2$ fermionic string theory is revisited in light of its recently proposed equivalence to the non-compact $N=4$ fermionic string model. The issues of space-time Lorentz covariance and supersymmetry for the BRST quantized $N=2$ strings living in uncompactified $2+2$ dimensions are discussed. The equivalent local quantum supersymmetric field theory appears to be the most transparent way to represent the space-time symmetries of the extended fermionic strings and their interactions. Our considerations support the Siegel's ideas about the presence of $SO(2,2)$ Lorentz symmetry as well as at least one self-dual space-time supersymmetry in the theory of the $N=2(4)$ fermionic strings, though we do not have a compelling reason to argue about the necessity of the {\it maximal} space-time supersymmetry. The world-sheet arguments about the absence of all string massive modes in the physical spectrum, and the vanishing of all string-loop amplitudes in the Polyakov approach, are given on the basis of general consistency of the theory.

29 pages, LaTeX, ITP-UH-1/93

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• $N=2$ Super-Weyl Symmetry, Super-Liouville Theory and Super-Riemannian Surfaces
• Dirac equation in (1+3) and (2+2) dimensions
• Integration Measure and Spectral Flow in the Critical N=2 String