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arXiv · hep-th/9207042

Self-Dual Supersymmetry and Supergravity in Atiyah-Ward Space-Time

Sergei V. Ketov·Hitoshi Nishino·S. James Gates, Jr
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Abstract

We study supersymmetry and self-duality in a four-dimensional space-time with the signature (2,2), that we call the Atiyah-Ward space-time. Dirac matrices and spinors, in particular Majorana-Weyl spinors, are investigated in detail. We formulate $ N\ge 1 $ supersymmetric self-dual Yang-Mills theories and self-dual supergravities. An N=1 ``self-dual'' tensor multiplet is constructed and a possible ten-dimensional theory that gives rise to the four-dimensional self-dual supersymmetric theories is found. Instanton solutions are given as the zero modes in the N=2 self-dual Yang-Mills theory. The N=2 superstrings are conjectured to have no possible counter-terms at quantum level to all orders. These self-dual supersymmetric theories are to generate exactly soluble supersymmetric systems in lower dimensions.

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Sergei V. Ketov, Hitoshi Nishino, S. James Gates, Jr. 1992-07-22. Self-Dual Supersymmetry and Supergravity in Atiyah-Ward Space-Time. https://doi.org/10.1016/0550-3213(93)90242-h

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