Chand Devchand, Viktor Ogievetsky
Four Dimensional Integrable Theories
Preprint series: ESI preprints

MSC:

81R25 Spinor and twistor methods, See also {32L25}

81T13 Yang-Mills and other gauge theories, See also {53C07,

81T60 Supersymmetric field theories

Abstract: There exist many four dimensional integrable theories. They include
self-dual gauge and gravity theories, all their extended supersymmetric
generalisations, as well the full (non-self-dual) N=3 super Yang-Mills
equations. We review the harmonic space formulation of the twistor
transform for these theories which yields a method of producing explicit
connections and metrics. This formulation uses the concept of harmonic space
analyticity which is closely related to that of quaternionic analyticity.

Keywords: Integrable theory, Yang-Mills theory, twistor transform