Action for N=4 supersymmetric self-dual Yang-Mills theory.

The N = 4 supersymmetric self-dual Yang-Mills theory in a four-dimensional space with signature (2, 2) is formulated in harmonic superspace. The on-shell constraints of the theory are reformulated in the equivalent form of vanishing curvature conditions for three gauge connections (one harmonic and two space-time). The constraints are then obtained as variational equations from a superspace action of the Chern-Simons type. The action is manifestly SO(2, 2) invariant. It can be viewed as the Lorentz-covariant form of the light-cone superfield action proposed by Siegel. ENSLAPP-A-545/95 September 1995 URA 14-36 du CNRS, associée à l’Ecole Normale Supérieure de Lyon et à l’Université de Savoie 1 Groupe d’Annecy: LAPP, Chemin de Bellevue BP 110, F-74941 Annecy-le-Vieux Cedex, France. a e-mail address: [email protected]