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arXiv 2012.00051hep-thmath-phmath.MP
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复合流的高群对称性场论

Field theories with higher-group symmetry from composite currents

Tomas Brauner

摘要:

更高形式的对称与只作用于扩展对象而不作用于点粒子的变换相关联。一般来说,高阶形式对称性与普通的点粒子(0-形式)对称性共存,它们可以用直积对称群来共同描述。然而,当0-形式和更高形式对称的作用纠缠在一起时,需要一个更一般的数学结构,与更高范畴群相关。具有连续高群对称性的系统以前是以自上而下的方式构造的,从具有特定混合特胡夫特反常的量子场论发展而来。我表明,更高的群对称性也自然出现从自下而上,低能量的角度来看,当物理系统在手头上包含至少两个不同的给定的,自发破缺的对称性。这一般导致了涌现的高级形式对称的层次结构,对应于该理论的拓扑流的格拉斯曼代数,具有潜在的高级群结构。具有这种更高群对称性的物理系统的例子包括超流体混合物和轴子电动力学的变体。

英文摘要:

Higher-form symmetries are associated with transformations that only act on extended objects, not on point particles. Typically, higher-form symmetries live alongside ordinary, point-particle (0-form), symmetries and they can be jointly described in terms of a direct product symmetry group. However, when the actions of 0-form and higher-form symmetries become entangled, a more general mathematical structure is required, related to higher categorical groups. Systems with continuous higher-group symmetry were previously constructed in a top-down manner, descending from quantum field theories with a specific mixed 't Hooft anomaly. I show that higher-group symmetry also naturally emerges from a bottom-up, low-energy perspective, when the physical system at hand contains at least two different given, spontaneously broken symmetries. This leads generically to a hierarchy of emergent higher-form symmetries, corresponding to the Grassmann algebra of topological currents of the theory, with an underlying higher-group structure. Examples of physical systems featuring such higher-group symmetry include superfluid mixtures and variants of axion electrodynamics.

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