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Topological Operators and Completeness of Spectrum in Discrete Gauge Theories

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arxiv 2006.10052 v2 pith:OA5AEIQD submitted 2020-06-17 hep-th

Tom Rudelius , Shu-Heng Shao This is my paper
classification hep-th
keywords gaugeoperatorstopologicalabsencecompletenessglobalspectrumtheory
verification ladder T0 review T1 audit T2 compute T3 formal
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In many gauge theories, the existence of particles in every representation of the gauge group (also known as completeness of the spectrum) is equivalent to the absence of one-form global symmetries. However, this relation does not hold, for example, in the gauge theory of non-abelian finite groups. We refine this statement by considering topological operators that are not necessarily associated with any global symmetry. For discrete gauge theory in three spacetime dimensions, we show that completeness of the spectrum is equivalent to the absence of certain Gukov-Witten topological operators. We further extend our analysis to four and higher spacetime dimensions. Since topological operators are natural generalizations of global symmetries, we discuss evidence for their absence in a consistent theory of quantum gravity.

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Cited by 3 Pith papers

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