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Title: Non-invertible global symmetries and completeness of the spectrum
A bstract 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.  more » « less
Award ID(s):
1911298 1914934
NSF-PAR ID:
10313114
Author(s) / Creator(s):
; ; ; ; ;
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2021
Issue:
9
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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