Higher-dimensional WZW Model on Kähler Manifold and Toroidal Lie Algebra
Takeo Inami, Hiroaki Kanno, Tatsuya Ueno
Abstract
We construct a generalization of the two-dimensional Wess-Zumino-Witten model on a 2n-dimensional Kähler manifold as a group-valued non-linear sigma model with an anomaly term containing the Kähler form. The model is shown to have an infinite-dimensional symmetry which generates an n-toroidal Lie algebra. The classical equation of motion turns out to be the Donaldson-Uhlenbeck-Yau equation, which is a 2n-dimensional generalization of the self-dual Yang-Mills equation.
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