Topological operators and completeness of spectrum in discrete gauge theories
Topological operators and completeness of spectrum in discrete gauge theories
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DOI：
10.1007/jhep12(2020)172
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发表时间：
2020-06
影响因子：
5.4
通讯作者：
Tom Rudelius;Shu-Heng Shao
中科院分区：
文献类型：
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作者：
Tom Rudelius;Shu-Heng Shao
在许多规范理论中，在规范群的每一个表示中粒子的存在（也称为谱的完备性）等价于不存在单一形式的整体对称。然而，这种关系并不成立，例如，在非阿贝尔有限群的规范理论。我们通过考虑不一定与任何全局对称性相关联的拓扑算子来完善这一陈述。对于三维时空中的离散规范理论，我们证明了谱的完备性等价于不存在某些Gukov-Witten拓扑算子。我们进一步扩展我们的分析，以四个更高的时空维度。由于拓扑算子是整体对称性的自然推广，我们讨论了它们在量子引力的一致性理论中不存在的证据。
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.