Affine Yang-Mills theory and affine self-dual Chern-Simons Solitons

A four-dimensional affine Yang-Mills theory, i.e. Yang—Mills gauge theory with values in an affine Kac-Moody algebra, is constructed which can give rise to a spontaneous breakdown of the affine symmetry. The affine self-dual Yang-Mills equation (which is a special kind of affine YM theory) in four dimensions is dimensionally reduced to the affine self-dual Chem-Simons equation in two dimensions. The latter is shown to have soliton solutions which satisfy the conformal affine Toda equations.K. C. Wong Research Award Winner; address after 28 October 1992: Department of Mathematics, University of Queensland, Brisbane, Queensland 4072, Australia.