Higher-Dimensional WZW Model on Kähler Manifold and Toroidal Lie Algebra

Abstract

We construct a generalization of the two-dimensional Wess–Zumino–Witten model on a 2n-dimensional Kähler manifold as a group-valued nonlinear 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.