The properties of Dirac gamma matrices in a four-dimensional space-time with the (2, 2) signature are studied. The basic spinors are classified, and the existence of Majorana-Weyl spinors is noted. Supersymmetry in 2+2 dimensions is discussed, and the existence of the real chiral scalar supermultiplet is discovered. Supersymmetric self-dual Yang-Mills theories and self-dual supergravity model in 2+2 dimensions, that are apparently relevant to integrable systems, are formulated for the first time.
ASJC Scopus subject areas
- Nuclear and High Energy Physics