A non-perturbative mixed anomaly and fractional hydrodynamic transport

Davighi, Joe; Lohitsiri, Nakarin; Poovuttikul, Napat

Abstract

We present a new non-perturbative ’t Hooft anomaly afflicting a quantum field theory with symmetry group G = U(1) × ℤ2 in four dimensions. We use the Adams spectral sequence to compute that the bordism group (BG), which classifies anomalies that remain when perturbative anomalies cancel, is ℤ4. By constructing a mapping torus and evaluating the Atiyah-Patodi-Singer η-invariant, we show that the mod 4 anomaly is generated by a pair of Weyl fermions that are vector-like under U(1), but with only one component charged under ℤ2. We construct a simple microscopic field theory that realises the anomaly, before investigating its impact in the hydrodynamic limit. We find that the anomaly dictates transport phenomena in the U(1) current and energy-momentum tensor akin to the chiral vortical and magnetic effects (even though the perturbative anomalies here vanish), but with the conductivities being fractionally quantised in units of a quarter, reflecting the mod 4 nature of the bordism group. Along the way, we compute the (relevant) bordism groups (Bℤ2 × BU(1)) and (BU(1)) in all degrees d = 0 through 5.

Citation

Davighi, J., Lohitsiri, N., & Poovuttikul, N. (2024). A non-perturbative mixed anomaly and fractional hydrodynamic transport. Journal of High Energy Physics, 2024(3), 42-55. https://doi.org/10.1007/jhep03%282024%29119

• Journal Article Type: Article
• Acceptance Date: Feb 25, 2024
• Online Publication Date: Mar 20, 2024
• Publication Date: Mar 20, 2024
• Deposit Date: Apr 16, 2024
• Publicly Available Date: Apr 16, 2024
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2024
• Issue: 3
• Article Number: 119
• Pages: 42-55
• DOI: https://doi.org/10.1007/jhep03%282024%29119
• Keywords: Topological States of Matter, Field Theory Hydrodynamics, Anomalies in Field and String Theories
• Public URL: https://durham-repository.worktribe.com/output/2385406