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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 = ∂/∂xμ is the partial derivative and the usual summation convention over indices is used, with an Euclidean metric. Here, is the Killing form on g, and thus the first term is the standard kinetic term of quantum field theory.


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