The N=2 super-Wess–Zumino–Novikov–Witten model valued in superdiffeomorphism (SDIFF) M2 is self-dual supergravity in four dimensions

Abstract

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.