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Toric 2-group anomalies via cobordism


Davighi, Joe; Lohitsiri, N; Debray, A (2023). Toric 2-group anomalies via cobordism. Journal of High Energy Physics, 07:19.

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 ΩSpin 5 (B|G|) ∼= 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

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 ΩSpin 5 (B|G|) ∼= 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

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > Nuclear and High Energy Physics
Language:English
Date:2023
Deposited On:05 Jan 2024 13:06
Last Modified:30 Jun 2024 01:36
Publisher:Springer
ISSN:1029-8479
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/JHEP07(2023)019
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)