Twistor-Like Formulation of Heterotic Strings

Abstract

In this talk new formulations of the Green--Schwarz heterotic strings in $D$ dimensions that involve commuting spinors, are reviewed. These models are invariant under $n$--extended, world sheet supersymmetry as well as under $N=1$, target space supersymmetry where $n\leq D-2$ and $D=3,4,6,10$. The world sheet supersymmetry replaces $n$ components (and provides a geometrical meaning) of the $\kappa$--symmetry in the Green--Schwarz approach. The models in $D=10$ for $n=1,2,8$ are discussed explicitly.