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Toric 2-group anomalies via cobordism.
- Source :
-
Journal of High Energy Physics . Jul2023, Vol. 2023 Issue 7, p1-54. 54p. - Publication Year :
- 2023
-
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|픾| where 픾 is any 2-group whose 0-form and 1-form symmetry parts are both U(1), and |픾| is the geometric realisation of the nerve of the 2-group 픾. By leveraging a variety of algebraic methods, we show that Ω 5 Spin B G ≅ ℤ / m where m is the modulus of the Postnikov class for 픾, 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 FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 11266708
- Volume :
- 2023
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Journal of High Energy Physics
- Publication Type :
- Academic Journal
- Accession number :
- 170391670
- Full Text :
- https://doi.org/10.1007/JHEP07(2023)019