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The Wess-Zumino term for a harmonic map

Nigel Hitchin
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Abstract

We calculate the Wess-Zumino term $Γ(g)$ for a harmonic map $g$ of a closed surface to a compact, simply connected, simple Lie group $G$ in terms of the energy and the holonomy of the Chern-Simons line bundle on the moduli space of flat $G$-connections. In the case of the 2-sphere we deduce that $Γ(g)$ is 0 or $π$ and for the 2-torus and $G=SU(2)$ we give a formula involving hyperelliptic integrals.

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Nigel Hitchin. 2000-08-04. The Wess-Zumino term for a harmonic map. https://arxiv.org/abs/math/0008038

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