From N=2 Fermionic Strings to Superstrings?

Abstract

I review the covariant quantization of the critical $N{=}2$ fermionic string with and without a global ${\bf Z}_2$ twist. The BRST analysis yields massless bosonic and fermionic vertex operators in various ghost and picture number sectors, as well as picture-changers and their inverses, depending on the field basis chosen for bosonization. Two distinct GSO projections exist, one (untwisted) retaining merely the known bosonic scalar and its spectral-flow partner, the other (twisted) yielding two fermions and one boson, on the massless level. The absence of interactions in the latter case rules out standard spacetime supersymmetry. In the untwisted theory, the $U(1,1)$-invariant three-point and vanishing four-point functions are confirmed at tree level. I comment on the $N{=}2$ string field theory, the integration over moduli and the realization of spectral flow.