Higher-dimensional WZW Model on K\"ahler Manifold and Toroidal Lie Algebra

TL;DR

This paper generalizes the 2D Wess-Zumino-Witten model to higher even dimensions on K"ahler manifolds, revealing an infinite-dimensional symmetry related to toroidal Lie algebras and connecting to higher-dimensional gauge equations.

Contribution

It introduces a higher-dimensional WZW model on K"ahler manifolds with a novel symmetry structure and links to generalized gauge equations.

Findings

Model exhibits infinite-dimensional toroidal Lie algebra symmetry.

Classical equations correspond to higher-dimensional Donaldson-Uhlenbeck-Yau equations.

Generalizes 2D WZW model to 2n dimensions with anomaly term.

Abstract

We construct a generalization of the two-dimensional Wess-Zumino-Witten model on a $2n$-dimensional K\"ahler manifold as a group-valued non-linear sigma model with an anomaly term containing the K\"ahler 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.