Self Dual Structure of Conformal Supergravity

On the basis of a unified definition of the dual operation and the (anti)self dual operation, the connections of the su(2,2｜1) main cluster was used as the fundamental field variables to construct the self dual Lagrangian of conformal supergravity. A Yang Mill like Lagrangian is obtained and a new gauge theory of supergravity is put forward. The spatial projects of its spin connection are Ashtekar variables.