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In this note we realise current algebra with anomalous terms in terms of a $U(1)$ gauge theory, in the space of maps $M$ from $S^1$ into a compact Lie group corresponding to the current algebra. The Wilson loop around a closed curve in $M$ is shown to be the Wess–Zumino–Witten term. This discussion enables a simple understanding of the non-Abelian anomaly in the Schrödinger picture.

Current algebra, a U(1) gauge theory and the Wess–Zumino–Witten model