Abstract
Affine CS and WZNW theories with values in infinite-dimensional (loop) groups are proposed. It appears that the affine CS theory naturally introduces a spectral parameter into a CS theory. The Sinh-Gordon, KdV, and nonlinear Schrödinger equations are obtained, via Hamiltonian reductions, from the affine WZNW. It is shown that the self-dual Yang-Mills (SDYM) equation is related to the equation of motion of the affine WZNW and, thus, symmetry algebra underlying the SDYM can be identified with the affine two-loop Kac-Moody algebra of the affine WZNW.
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K. C. Wong Research Award Winner, address after 28 October 1992: Department of Mathematics, University of Queensland, Brisbane, Queensland 4072, Australia.
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Zhang, YZ. Loop Group-Valued CS and WZNW models, integrable systems, and self-dual Yang-Mills theory. Lett Math Phys 26, 227–233 (1992). https://doi.org/10.1007/BF00420756
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DOI: https://doi.org/10.1007/BF00420756