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

Abstract 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 di...

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Bibliographic Details
Published inProgress of theoretical and experimental physics Vol. 2021; no. 8
Main Author Wadia, Spenta R
Format Journal Article
LanguageEnglish
Published Oxford Oxford University Press 01.08.2021
Subjects
Algebra
Lie groups
Quarks
B31
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Summary:Abstract 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.
Bibliography:ObjectType-Article-1
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ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptab021