论文标题
离散量规理论中的拓扑操作员和光谱的完整性
Topological Operators and Completeness of Spectrum in Discrete Gauge Theories
论文作者
论文摘要
在许多规格的理论中，量规组的每个表示中的粒子的存在（也称为光谱的完整性）等同于缺乏单一的全局对称性。但是，这种关系在非亚伯有限群体的规格理论中不存在。我们通过考虑不一定与任何全球对称性相关的拓扑操作员来完善这一说法。对于三个时空维度中的离散仪表理论，我们表明频谱的完整性等同于缺乏某些古科夫（Gukov）编织的拓扑操作员。我们将分析进一步扩展到四个及更高的时空维度。由于拓扑操作员是全球对称性的自然概括，因此我们讨论了证据在一致的量子重力理论中缺乏的证据。
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.
