Non-invertible global symmetries and completeness of the spectrum

• Main Authors: Ben Heidenreich, Jacob McNamara, Miguel Montero, Matthew Reece, Tom Rudelius, Irene Valenzuela
• Format: Article
• Language: English
• Published: SpringerOpen 2021-09-01
• Series: Journal of High Energy Physics
• Subjects: Gauge Symmetry; Global Symmetries; Topological Field Theories; Effective Field Theories
• Online Access: https://doi.org/10.1007/JHEP09(2021)203

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.