MAJORANA-WEYL SPINORS AND SELF-DUAL GAUGE-FIELDS IN 2+2 DIMENSIONS

The properties of Dirac gamma matrices in a four-dimensional space-tim e with the (2, 2) signature are studied. The basic spinors are classif ied, and the existence of Majorana-Weyl spinors is noted. Supersymmetr y in 2 + 2 dimensions is discussed, and the existence of the real chir al scalar supermultiplet is discovered. Supersymmetric self-dual Yang- Mills theories and self-dual supergravity model in 2 + 2 dimensions, t hat are apparently relevant to integrable systems, are formulated for the first time.