Twistor transform of yang-mills theory

Abstract

Twistor theory is an attempt at the synthesis of quantum theory and general relativity, with use of complex geometrical analysis. We describe the geometrical correspondences between space-time and twistor space. The massless free fields are expressed by the contour integral of holomorphic twistor functions. It is shown that there is the twistor transform of self-dual Yang-Mills theory. Extending to supersymmetry, we introduce supertwistors and construct the twistor transform of D=4, N=1 supersymmetric Yang-Mills theory.