非阿贝尔任意子的增殖跃迁注记
Note on proliferation transitions of non-Abelian anyons
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中文总结 AI 辅助
该研究构建了拓扑相增殖跃迁的通用理论框架，结合SymTFT阐释其构造，给出CSH场论实例，还实现了非可逆一维对称性的规范，明确了相关任意子的增殖情况。
中文摘要 AI 辅助
我们研究由辫化融合子范畴中任意子增殖所驱动的（2+1）维拓扑相的相变。我们为此类跃迁描述了一个通用理论框架，其中拓扑量子场论（TQFT）与子范畴中任意子相关的动力学物质耦合。我们利用对称拓扑场论（SymTFT）阐释这一构造，其中动力学定域于（3+1）维平板的对称边界上。我们分析了若干实例，给出了实现增殖跃迁的明确陈-西蒙斯-希格斯（CSH）场论，还研究了在母TQFT中实现非可逆一维对称性规范的增殖跃迁，包括有限群G的Rep(G)一维对称性的通用构造，以及非可逆一维规范SU(2)₁₀→Spin(5)₁的CSH实现。我们讨论了这些跃迁中哪些任意子会发生增殖。
英文摘要
We study phase transitions out of a (2+1)d topological phase driven by the proliferation of anyons in a braided fusion subcategory. We describe a general theoretical framework for such transitions, in which the topological quantum field theory (TQFT) is coupled to dynamical matter associated with anyons in the subcategory. We interpret this construction using symmetry topological field theory (SymTFT), where the dynamics is localized on the symmetry boundary of the (3+1)d slab. We analyze several examples, and present explicit Chern-Simons-Higgs (CSH) field theories realizing the proliferation transitions. We also examine proliferation transitions that implement gauging of non-invertible one-form symmetry in the parent TQFT. This includes a general construction for ${\rm Rep}(G)$ one-form symmetry for a finite group $G$, and a CSH realization of the non-invertible one-form gauging ${\rm SU}(2)_{10}\rightarrow {\rm Spin}(5)_1$. We discuss which anyons proliferate at these transitions.
