Revisiting Wess-Zumino-Witten terms

@article{Lee2020RevisitingWT,
  title={Revisiting Wess-Zumino-Witten terms},
  author={Yasunori Lee and Kantaro Ohmori and Yuji Tachikawa},
  journal={arXiv: High Energy Physics - Theory},
  year={2020}
}
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. 
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