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

TL;DR

This paper reviews a string theory formulated in $(x, heta)$ space specifically for self-dual ${ m N}=4$ super-Yang-Mills, aiming to connect twistor-string models with the pure spinor formalism of superstrings.

Contribution

It constructs a novel string theory in $(x, heta)$ space for self-dual ${ m N}=4$ super-Yang-Mills, providing insights into twistor-string and pure spinor formalisms.

Findings

Provides a string theory in $(x, heta)$ space for self-dual ${ m N}=4$ SYM

Suggests potential links between twistor-string models and pure spinor formalism

Aims to deepen understanding of superstring theories in twistor space

Abstract

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 $(x,\theta)$ 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.