Off-Shell Supersymmetry versus Hermiticity in Superstrings.

Superstring theory is the only known renormalizable quantum theory of gravity, and spacetime supersymmetry plays a crucial role in removing the divergences. Spacetime supersymmetry also plays a crucial role in the recent conjectures [1] of strong-weak duality in superstring theory. However, spacetime supersymmetry is only an on-shell symmetry in the conventional N ­ 1 RamondNeveu-Schwarz (RNS) description of the superstring, which makes it difficult to observe its effects. It will be shown in this Letter that after modifying the conventional Hermiticity properties, four-dimensional supersymmetry can be extended to an off-shell symmetry of the superstring. The modified Hermiticity properties are those of an N ­ 2 embedding of the N ­ 1 RNS superstring [2], where N ­ 1 and N ­ 2 refer to the number of worldsheet superconformal invariances. This suggests that the N ­ 2 description of the superstring [3] may be useful for illuminating the effects of spacetime supersymmetry. It is interesting to note that N ­ 2 superstrings have recently appeared in models [4] which try to explain the strong-weak duality symmetries. In four-dimensional compactifications of the N ­ 1 RNS superstring, the spacetime-supersymmetry generators in the 2 12 picture are