WZW terms without anomalies: Generalised symmetries in chiral Lagrangians

Davighi, Joe; Lohitsiri, Nakarin

Abstract

We consider a 4d non-linear sigma model on the coset (SU(N)L × SU(N)R × SU(2))/(SU(N)L+R × U(1)) ∼= SU(N) × S
2, that features a topological Wess–Zumino–Witten (WZW) term whose curvature is n/24π2 Tr(g−1dg )3 ∧ VolS2 where g is the SU(N)
pion field. This WZW term, unlike its familiar cousin in QCD, does not match any chiral anomaly, so its microscopic origin is not obviously QCD-like. We find that generalised symmetries provide a key to unlocking a UV completion. The S2 winding number bestows the theory with a 1-form symmetry, and the WZW term intertwines this with the SU(N)2 flavour symmetry into a 2-group global symmetry. Like a ’t Hooft anomaly, the 2-group symmetry should match between UV and IR, precluding QCD-like completions that otherwise give the right pion manifold. We instead construct a weakly-coupled UV
completion that matches the 2-group symmetry, in which an abelian gauge field connects the QCD baryon number current to the winding number current of a CP1 model, and explicitly show how the mixed WZW term arises upon flowing to the IR. The coefficient is
fixed to be the number of QCD colours and, strikingly, this matching must be ‘tree-level exact’ to satisfy a quantization condition. We discuss generalisations, and elucidate the more intricate generalised symmetry structure that arises upon gauging an anomalyfree subgroup of SU(N)L+R. This WZW term may even play a phenomenological role as a portal to a dark sector, that determines the relic abundance of dark matter.

Citation

Davighi, J., & Lohitsiri, N. (2024). WZW terms without anomalies: Generalised symmetries in chiral Lagrangians. SciPost Physics, 17(6), Article 168. https://doi.org/10.21468/scipostphys.17.6.168

• Journal Article Type: Article
• Acceptance Date: Nov 19, 2024
• Online Publication Date: Dec 13, 2024
• Publication Date: Dec 13, 2024
• Deposit Date: Jan 22, 2025
• Publicly Available Date: Jan 22, 2025
• Journal: SciPost Physics
• Print ISSN: 2542-4653
• Electronic ISSN: 2542-4653
• Publisher: SciPost
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 6
• Article Number: 168
• DOI: https://doi.org/10.21468/scipostphys.17.6.168
• Public URL: https://durham-repository.worktribe.com/output/3345452