Self-dual Yang-Mills (+gravity) as a 2D sigma model

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Abstract The 4D self-dual Yang-Mills gauge theory on a self-dual space X is shown to be equivalent to a 2D sigma model valued in infinite dimensional gauge groups. Infinitesimal symmetries of the self-dual equation are obtained in terms of the sheaf cohomology group H 1 ( T , O F (−2)) , of the twistor space T corresponding to X. They are shown to form a symmetry algebra - a “CP1-extension” of the gauge symmetry algebra of a 2D sigma model which generalizes the Kac-Moody algebra as well as Wt8.