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

Spenta R. Wadia | Zendy

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

Author(s) -

Spenta R. Wadia

Publication year - 2021

Publication title -

progress of theoretical and experimental physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.887

H-Index - 53

ISSN - 2050-3911

DOI - 10.1093/ptep/ptab021

Subject(s) - physics , current algebra , anomaly (physics) , mathematical physics , gauge theory , gauge (firearms) , abelian group , gauge group , current (fluid) , gauge anomaly , wess–zumino–witten model , term (time) , algebra over a field , quantum electrodynamics , hamiltonian lattice gauge theory , quantum mechanics , pure mathematics , mathematics , geometry , history , thermodynamics , conformal map , archaeology

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.

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