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 {\it real chiral} scalar supermultiplet is discovered. Supersymmetric {\it self-dual} Yang-Mills theories and {\it self-dual} supergravity model in $2+2$ dimensions, that are apparently relevant to integrable systems, are formulated for the first time.

15 pages

References in corpus (2)

• Self-Dual Supersymmetry and Supergravity in Atiyah-Ward Space-Time
• Supersymmetric Self-Dual Yang-Mills and Supergravity as Background of Green-Schwarz Superstring

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