THE N=2 SUPER-WESS-ZUMINO-NOVIKOV-WITTEN MODEL VALUED IN SUPERDIFFEOMORPHISM (SDIFF) M(2) IS SELF-DUAL SUPERGRAVITY IN 4 DIMENSIONS

It is shown that the pure topological term of the N = 2 super-Wess-Zumino-Novikov-Witten (SWZNW) model, valued in the area-preserving diffeomorphisms group of a two-dimensional Euclidean surface, is self-dual supergravity (SDSG) in 3 + 1 dimensions. This is achieved by a suitable slicing and pasting procedure of the (2,0); (0,2) N = 2 SWZNW models determined by the embedding of the (2,0); (0,2) superspace supercovariant derivatives into the (3 + 1) superspace ones. Preliminary steps are provided to show that the N = 1 SWZNW model, valued in the area-preserving superdiffeomorphism group of a super Riemann surface (SRS) whose signature is (1 + 1), is self-dual supergravity in (2 + 2) dimensions: the so-called Atiyah-Ward space-times.