Revisiting Wess-Zumino-Witten terms

Abstract

We revisit various topological issues concerning four-dimensional ungauged and gauged Wess-Zumino-Witten (WZW) terms for $SU$ and $SO$ quantum chromodynamics (QCD), from the modern bordism point of view. We explain, for example, why the definition of the $4d$ WZW terms requires the spin structure. We also discuss how the mixed anomaly involving the 1-form symmetry of $SO$ QCD is reproduced in the low-energy sigma model.

arXiv comment59 pages; v2: minor changes

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• Stable Vacua for Tachyonic Strings
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• Spin Statistics and Surgeries of Topological Solitons in QCD Matter in Magnetic Field
• What bordism-theoretic anomaly cancellation can do for U
• Anomalous continuous symmetries and quantum topology of Goldstone modes
• Instanton Density Operator in Lattice QCD from Higher Category Theory
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• WZW terms without anomalies: generalised symmetries in chiral Lagrangians
• Cancelling mod-2 anomalies by Green-Schwarz mechanism with $B_{\mu \nu }$