论文标题
断开的0形和2组对称性
Disconnected 0-Form and 2-Group Symmetries
论文作者
论文摘要
量子场理论可以具有连续和有限的0形式对称性。我们研究存在两种0形式对称性时出现的全局对称结构。与连续0形式对称性相关的全局结构由连接的谎言组描述，该基团捕获了连续0形式对称性的可能背景，该理论可以耦合。有限的0形式对称性可以充当该连接的谎言组的外部自动形态。因此，与连续的谎言组描述了连续和有限0形式对称性的可能背景耦合，我们称结果对称结构为脱节的0形式对称性。另外，有限的0形式对称性可以作用于1形对称组。 1形式的对称性和连续0形式的对称性可以组合形成一个2组，当与有限的0形式对称性结合时，该组将导致另一种类型的2组，我们称之为脱节的2组，而所产生的对称结构是不连续的2组对称性的。 Examples of arbitrarily complex disconnected 0-form and 2-group symmetries in any spacetime dimension are furnished by gauge theories: with 1-form symmetries arising from the center of the gauge group, continuous 0-form symmetries arising as flavor symmetries acting on matter content, and finite 0-form symmetries arising from outer-automorphisms of gauge and flavor Lie algebras.
Quantum field theories can have both continuous and finite 0-form symmetries. We study global symmetry structures that arise when both kinds of 0-form symmetries are present. The global structure associated to continuous 0-form symmetries is described by a connected Lie group, which captures the possible backgrounds of the continuous 0-form symmetries the theory can be coupled to. Finite 0-form symmetries can act as outer-automorphisms of this connected Lie group. Consequently, possible background couplings to both continuous and finite 0-form symmetries are described by a disconnected Lie group, and we call the resulting symmetry structure a disconnected 0-form symmetry. Additionally, finite 0-form symmetries may act on the 1-form symmetry group. The 1-form symmetries and continuous 0-form symmetries may combine to form a 2-group, which when combined with finite 0-form symmetries leads to another type of 2-group, that we call a disconnected 2-group and the resulting symmetry structure a disconnected 2-group symmetry. Examples of arbitrarily complex disconnected 0-form and 2-group symmetries in any spacetime dimension are furnished by gauge theories: with 1-form symmetries arising from the center of the gauge group, continuous 0-form symmetries arising as flavor symmetries acting on matter content, and finite 0-form symmetries arising from outer-automorphisms of gauge and flavor Lie algebras.
