Anomalies of non-Abelian finite groups via cobordism

Journal of High Energy Physics

Regular Article - Theoretical Physics

Ben Gripaios¹  Nakarin Lohitsiri²  Joe Davighi³ 

[1] Cavendish Laboratory, University of Cambridge, Cambridge, UK;Department of Mathematical Sciences, Durham University, Durham, UK;Physics Institute, University of Zurich, Zurich, Switzerland;

关键词: Anomalies in Field and String Theories;    Discrete Symmetries;    Theories of Flavour;    Topological Field Theories;   

DOI  :  10.1007/JHEP09(2022)147

 received in 2022-08-08, accepted in 2022-09-06,  发布年份 2022

来源: Springer

【 摘 要 】

We use cobordism theory to analyse anomalies of finite non-abelian symmetries in 4 spacetime dimensions. By applying the method of ‘anomaly interplay’, which uses functoriality of cobordism and naturality of the η-invariant to relate anomalies in a group of interest to anomalies in other (finite or compact Lie) groups, we derive the anomaly for every representation in many examples motivated by flavour physics, including S3, A4, Q8, and SL(2, ?3).In the case of finite abelian groups, it is well known that anomalies can be ‘truncated’ in a way that has no effect on low-energy physics, by means of a group extension. We extend this idea to non-abelian symmetries. We show, for example, that a system with A4 symmetry can be rendered anomaly-free, with only one-third as many fermions as naïvely required, by passing to a larger symmetry. As another example, we find that a well-known model of quark and lepton masses utilising the SL(2, ?3) symmetry is anomalous, but that the anomaly can be cancelled by enlarging the symmetry to a ℤ/3 extension of SL(2, ?3).

【 授权许可】

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© The Author(s) 2022