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Different string theories in twistor space have recently been proposed fordescribing ${\cal N}=4$ super-Yang-Mills. In this paper, my Strings 2003 talkis reviewed in which a string theory in $(x,\theta)$ space was constructed forself-dual ${\cal N}=4$ super-Yang-Mills. It is hoped that these results will beuseful for understanding the twistor-string proposals and their possiblerelation with the pure spinor formalism of the $d=10$ superstring.Comment: Strings 2003 proceedings, 14 page

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