A new symmetry group of real self-dual Yang-Mills theory

A new infinite parameter symmetry group is found for real self-dual Yang-Mills theory in four euclidean dimensions. Whereas the gauge potentials transform under a group including local gauge transformations and Kac-Moody-like transformations, the gauge invariant object tr P exp(∮A·dξ) is seen to carry a representation of the Kac-Moody symmetry. Four-dimensional Polyakov loop-space currents restricted to the self-dual sector are constructed from this algebra.