## Abstract

This paper is a survey of results relating the supertwistor correspondence on N-extended super-Minkowski space M^{4|4N} to supersymmetric Yang-Mills (SSYM) theory. A theorem of Manin relating bundles on the (3-N)th infinitesimal neighborhood L_{(3-N)}^{5|2N} of super null-line space L^{ 5 2N}→P^{ 3 N}×P^{ 3 N*} to solutions of the SSYM equations is analyzed in terms of component fields, interpolating between the N = 0 and N = 3 results studied previously. Using an inductive approach based on the degree of odd homogeneity and a particular gauge condition (the D-gauge), the graded Frobenius equations for covariant constancy along super null-lines are solved. The resulting solution space is shown to define a bundle over L^{5|2N} which extends to L_{(3-N)}^{5|2N} when the SSYM equations are satisfied. Conversely, the inverse transform determines super connections that are integrable along super null-lines in M^{4|4N}. These superconnections determine a supermultiplet which solves the SSYM equations when the bundle over L^{5|2N} extends to L_{(3-N)}^{5|2N}. A clarification is given concerning the relation between supersymmetry transformations of the component fields and Lie derivations of superconnections on M^{4|4N} satisfying super null-line integrability conditions and the D-gauge conditions. Our approach is aimed at bridging the gap between the abstract sheaf-theoretic formulation preferred by mathematicians and the coordinate formulation familiar to physicists.

Original language | English |
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Pages (from-to) | 40-79 |

Number of pages | 40 |

Journal | Annals of Physics |

Volume | 193 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1989 |

Externally published | Yes |

### Bibliographical note

Funding Information:in part by the Natural of Science.

### Funding

in part by the Natural of Science.

Funders | Funder number |
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Natural of Science |