### 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 ≥ 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 in lower dimensions.

Original language | English |
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Pages (from-to) | 149-210 |

Number of pages | 62 |

Journal | Nuclear Physics, Section B |

Volume | 393 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 22 Mar 1993 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*393*(1-2), 149-210. https://doi.org/10.1016/0550-3213(93)90242-H