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

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

1992-07-13

arxiv.org/abs/hep-th/9207042v3

Nucl.Phys. B393 (1993) 149-210

Physics

High Energy Physics

High Energy Physics - Theory

61 pages

Scientific paper

10.1016/0550-3213(93)90242-H

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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