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Self-Dual Super-Yang-Mills as a String Theory in $(x,θ)$ Space

Different string theories in twistor space have recently been proposed for describing ${\cal N}=4$ super-Yang-Mills. In this paper, my Strings 2003 talk is reviewed in which a string theory in $(x,θ)$ space was constructed for self-dual ${\cal N}=4$ super-Yang-Mills. It is hoped that these results will be useful for understanding the twistor-string proposals and their possible relation with the pure spinor formalism of the $d=10$ superstring.