Majorana-Weyl Spinors and Self-Duality Gauge Fields in 2+2 Dimensions
Abstract
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.
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