发表机构
Society of Fellows, Harvard University; Department of Physics, Harvard University; University of Colorado, Boulder（哈佛大学 fellowship 院; 哈佛大学物理系; 科罗拉多大学博尔德分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究基于共形嵌入的(2+1)维陈-西蒙斯希格斯化转变，揭示任意子增殖机制，提出未希格斯化相候选任意子，并构造Spin(16)1到Spin(9)2转变以探索非阿贝尔任意子凝聚。
AI 中文摘要
我们讨论了基于共形嵌入的(2+1)维陈-西蒙斯希格斯化转变及其与任意子增殖的关系。这些转变在减少规范群的同时保留或扩大了内禀拓扑序。当拓扑序扩大时，两个相通过任意子凝聚区分，转变将阿贝尔拓扑序变为非阿贝尔拓扑序。在$N \geq 3$的$SO(N)_{2} \hookrightarrow SU(N)_{1}$族中，两个半经典区域具有等价的内禀拓扑序，但全局$U(1)$对称性的实现不同。对于奇数$N$，这些是从费米子$1/N$劳克林态到电荷为$2e$的任意子超导性转变的非阿贝尔实现，且与相同的手征$\mathbb{Z}_{N}$拓扑序共存。标量表示相对于紫外陈-西蒙斯能级总是不可积的，因此尽管在紫外中定义了威尔逊线，它们并不直接标记未希格斯化相的任意子。利用启发式伴随屏蔽，我们提出了未希格斯化相中的候选任意子，而希格斯子群下的分支揭示了对应于希格斯相中可凝聚任意子的通道。我们进一步构造了一个$\mathrm{Spin}(16)_{1} \to \mathrm{Spin}(9)_{2}$转变，该转变允许一个包含非阿贝尔任意子但其自融合不包含所有允许的可规范通道的可凝聚代数。
英文摘要
We discuss (2+1)d Chern-Simons Higgsing transitions based on conformal embeddings and their relation to the proliferation of anyons. These transitions preserve or enlarge the intrinsic topological order despite reducing the gauge group. When the topological order is enlarged, the two phases differ by anyon condensation, and the transition takes an Abelian topological order to a non-Abelian one. In the $SO(N)_{2} \hookrightarrow SU(N)_{1}$ family with $N \geq 3$, the two semiclassical regimes have equivalent intrinsic topological orders but distinct realizations of a global $U(1)$ symmetry. For odd $N$, these are non-Abelian realizations of transitions from fermionic $1/N$ Laughlin states to charge-$2e$ anyon superconductivity coexisting with the same chiral $\mathbb{Z}_{N}$ topological order. The scalar representations are always non-integrable with respect to the UV Chern-Simons level and therefore do not directly label anyons of the un-Higgsed phase, despite defining Wilson lines in the UV. Using heuristic adjoint screening, we propose candidate anyons in the un-Higgsed phase, while branching under the Higgs subgroup reveals channels corresponding to condensable anyons of the Higgs phase. We further construct a $\mathrm{Spin}(16)_{1} \to \mathrm{Spin}(9)_{2}$ transition admitting a condensable algebra that contains a non-Abelian anyon but not all of the allowed gaugable channels in its self-fusion.
Comments15 pages, including 2 pages of End Matter and 6 pages of Supplemental Material
