ACTION FOR N=4 SUPERSYMMETRIC SELF-DUAL YANG-MILLS THEORY

The N = 4 supersymmetric self-dual Yang-Mills theory in four-dimension al space with the signature (2,2) is formulated in harmonic superspace . The on-shell constraints of the theory are reformulated in the equiv alent form of vanishing curvature conditions for three gauge connectio ns (one harmonic and two space-time). The constraints are then obtaine d as variational equations from a superspace action of the Chern-Simon s-type. The action is manifestly SO(2,2) invariant. It can be viewed a s the Lorentz-covariant form of the light-cone superfield action propo sed by Siegel.