论文标题
组成派助手：$ z_ {n} $分数量子厅系统的构造以及对拘留和二元性的现代理解
Composing parafermions: a construction of $Z_{N}$ fractional quantum Hall systems and a modern understanding of confinement and duality
论文作者
论文摘要
在这项工作中，我们提出了整数旋转简单电流的现代视图，该电流在离散扭转中发挥了核心作用。我们将它们重新引入为$ z_ {n} $ parafermionic field理论的非反式复合粒子。这些复合粒子与Bardeen-Cooper-Schrieffer理论中的库珀对有类似的比例，可以解释为Anyon冷凝的典型例子。基于这些$ z_ {n} $无异常的复合粒子，我们提出了$ z_ {n} $分数量子霍尔效应（FQHES）的气缸分区功能的系统构造。可以通过破坏这些FQH模型的骨骨部分的大块对应关系来期待一类通用拓扑排序系统的实现。我们还简要概述了当代冷凝物理物理学中各种现象，例如$ su（n）$ haldane猜想，一般间隙和间隙的拓扑顺序，相对于这些简单电流的指控定义的量子异常，以及这些简单电流，散装和边界重新划分组流动。此外，我们指出了这些FQHES和与物质结合的2D量子重力之间的类比，并提出了$ Z_ {N} $对综合偏屈理论中称为“分数超对称性”的超对称性的概括，并研究了其与Quark Collinement的类比。我们的分析以源自操作员形式主义的分区函数的形式对当代物理学进行了简单但一般的理解。
In this work, we propose a modern view of the integer spin simple currents which have played a central role in discrete torsion. We reintroduce them as nonanomalous composite particles constructed from $Z_{N}$ parafermionic field theories. These composite particles have an analogy with the Cooper pair in the Bardeen-Cooper-Schrieffer theory and can be interpreted as a typical example of anyon condensation. Based on these $Z_{N}$ anomaly free composite particles, we propose a systematic construction of the cylinder partition function of $Z_{N}$ fractional quantum Hall effects (FQHEs). One can expect realizations of a class of general topological ordered systems by breaking the bulk-edge correspondence of the bosonic parts of these FQH models. We also give a brief overview of various phenomena in contemporary condensed matter physics, such as $SU(N)$ Haldane conjecture, general gapless and gapped topological order with respect to the quantum anomaly defined by charges of these simple currents and bulk and boundary renormalization group flow. Moreover, we point out an analogy between these FQHEs and 2d quantum gravities coupled to matter, and propose a $Z_{N}$ generalization of supersymmetry known as "fractional supersymmetry" in the composite parafermionic theory and study its analogy with quark confinement. Our analysis gives a simple but general understanding of the contemporary physics of topological phases in the form of the partition functions derived from the operator formalism.
