Non-invertible global symmetries and completeness of the spectrum

Heidenreich, Ben; McNamara, Jacob; Montero, Miguel; Reece, Matthew; Rudelius, Tom; Valenzuela, Irene

Abstract

It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings.

Citation

Heidenreich, B., McNamara, J., Montero, M., Reece, M., Rudelius, T., & Valenzuela, I. (2021). Non-invertible global symmetries and completeness of the spectrum. Journal of High Energy Physics, 2021(9), Article 203. https://doi.org/10.1007/jhep09%282021%29203

• Journal Article Type: Article
• Acceptance Date: Sep 6, 2021
• Online Publication Date: Sep 29, 2021
• Publication Date: Sep 29, 2021
• Deposit Date: Apr 15, 2024
• Publicly Available Date: Apr 15, 2024
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2021
• Issue: 9
• Article Number: 203
• DOI: https://doi.org/10.1007/jhep09%282021%29203
• Keywords: Nuclear and High Energy Physics
• Public URL: https://durham-repository.worktribe.com/output/2384418