AI 中文总结
本文基于 Ginzburg-Landau 哲学，利用对称性拓扑场论，为不可逆对称性破缺相变建立场论描述，并以 Rep($S_3$) 对称性为例说明其关键步骤。
AI 中文摘要
最近，有人提出了一种广义的 Landau 范式，在该范式中，一大类超出 Landau 原始对称性破缺框架的“非传统”相变被理解为广义对称性的对称性破缺相变。特别是在 (1+1) 维中，此类“拓扑”或“去禁闭”相变可以映射到不可逆对称性的对称性破缺相变。如何从这种理解中提取相变的普适动力学性质？在本文中，我们遵循 Ginzburg-Landau 哲学，发展了一种场论描述，用于描述此类临界点，该描述基于局部序参量的涨落，现在这些序参量属于不可逆对称性。对称性拓扑场论形式在我们的分析中起着核心作用，使我们能够从 (2+1) 维拓扑序的 Lagrangian 代数中识别出局部序参量的代数。我们使用具有简单不可逆对称性——Rep($S_3$) 对称性——的有间隙相之间的相变，来说明这种广义 Ginzburg-Landau 过程的关键思想和完整步骤。
英文摘要
Recently, a generalized Landau paradigm has been proposed, in which a broad class of "unconventional" phase transitions lying beyond the original symmetry-breaking framework of Landau are understood as the symmetry-breaking transitions of generalized symmetries. In particular, in (1+1)D, such "topological" or "deconfined" transitions can be mapped to the symmetry-breaking transitions of non-invertible symmetries. How to extract the universal dynamical properties of the transitions from this understanding? In this paper, we follow the Ginzburg-Landau philosophy and develop a field-theoretic description of such critical points in terms of the fluctuations of local order parameters, now of non-invertible symmetries. The Symmetry Topological Field Theory formalism plays a central role in our analysis, allowing us to identify the algebra of local order parameters from the Lagrangian algebra of a (2+1)D topological order. We illustrate the key ideas and the full steps of this generalized Ginzburg-Landau procedure using the transitions between gapped phases with a simple non-invertible symmetry --- the Rep($S_3$) symmetry.
Comments20 pages, v1
