Wess-Zumino-Witten model

In theoretical physics and mathematics, a Wess–Zumino–Witten (WZW) model, also called a Wess–Zumino–Novikov–Witten model, is a type of two-dimensional conformal field theory named after Julius Wess, Bruno Zumino, Sergei Novikov and Edward Witten. The symmetry algebra of a WZW model is an affine Lie algebra.

Let G denote a compact simply-connected Lie group and g its simple Lie algebra. Suppose that γ is a G-valued field on the complex plane. More precisely, we want γ to be defined on the Riemann sphere S ², which amounts to the complex plane compactified by adding a point at infinity.

The WZW model is then a nonlinear sigma model defined by γ with an action given by

Here, ∂_μ = ∂/∂x^μ is the partial derivative and the usual summation convention over indices is used, with an Euclidean metric. Here, ${\displaystyle {\mathcal {K}}}$ is the Killing form on g, and thus the first term is the standard kinetic term of quantum field theory.

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