Toric 2-group anomalies via cobordism

Davighi, Joe; Lohitsiri, Nakarin; Debray, Arun

Abstract

2-group symmetries arise in physics when a 0-form symmetry G[0] and a 1-form symmetry H[1] intertwine, forming a generalised group-like structure. Specialising to the case where both G[0] and H[1] are compact, connected, abelian groups (i.e. tori), we analyse anomalies in such ‘toric 2-group symmetries’ using the cobordism classification. As a warm up example, we use cobordism to study various ’t Hooft anomalies (and the phases to which they are dual) in Maxwell theory defined on non-spin manifolds. For our main example, we compute the 5th spin bordism group of B|𝔾| where 𝔾 is any 2-group whose 0-form and 1-form symmetry parts are both U(1), and |𝔾| is the geometric realisation of the nerve of the 2-group 𝔾. By leveraging a variety of algebraic methods, we show that Ω5SpinBG≅ℤ/m where m is the modulus of the Postnikov class for 𝔾, and we reproduce the expected physics result for anomalies in 2-group symmetries that appear in 4d QED. Moving down two dimensions, we recap that any (anomalous) U(1) global symmetry in 2d can be enhanced to a toric 2-group symmetry, before showing that its associated local anomaly reduces to at most an order 2 anomaly, when the theory is defined with a spin structure.

Citation

Davighi, J., Lohitsiri, N., & Debray, A. (2023). Toric 2-group anomalies via cobordism. Journal of High Energy Physics, 2023(7), Article 19. https://doi.org/10.1007/jhep07%282023%29019

• Journal Article Type: Article
• Acceptance Date: Jun 10, 2023
• Online Publication Date: Jul 3, 2023
• Publication Date: 2023
• Deposit Date: Oct 9, 2023
• Publicly Available Date: Oct 9, 2023
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2023
• Issue: 7
• Article Number: 19
• DOI: https://doi.org/10.1007/jhep07%282023%29019
• Keywords: Global Symmetries, Anomalies in Field and String Theories
• Public URL: https://durham-repository.worktribe.com/output/1787845