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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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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ISSN2050-3911
2050-3911
DOI10.1093/ptep/ptab021

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Abstract 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.
AbstractList 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.
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.
Author Wadia, Spenta R
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10.1016/0370-2693(79)90027-3
10.1103/PhysRevD.10.2445
10.1103/PhysRevLett.52.959
10.1103/PhysRevD.31.3256
10.1016/0370-2693(79)90131-X
10.1016/0370-1573(80)90130-1
10.1103/PhysRevD.24.970
10.1016/0370-2693(77)90010-7
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10.1016/0550-3213(85)90632-7
10.1016/0370-2693(79)91193-6
10.1016/0550-3213(74)90154-0
ContentType Journal Article
Copyright The Author(s) 2021. Published by Oxford University Press on behalf of the Physical Society of Japan. 2021
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Snippet 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...
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...
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SubjectTerms Algebra
Lie groups
Quarks
Title Current algebra, a U(1) gauge theory and the Wess–Zumino–Witten model
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