论文标题
量子液体类别i
Categories of quantum liquids I
论文作者
论文摘要
我们根据Gaiotto和Johnson-Freyd在凝结完成方面的工作开发了可分离的高级类别的数学理论。基于这一理论，我们证明了$ e_m $ $ -Multi-Fusion更高类别及其更高中心的一些基本结果。我们还概述了基于$*$ - 凝结完成的统一高级类别的理论。在这些数学制备基于拓扑芯旋转的概念之后，我们开发了所有量子液体的统一数学理论，其中包括拓扑顺序，SPT/set订单，破坏对称性的订单和类似CFT的无间隙相。我们解释说，量子液体由拓扑骨架和局部量子对称性组成，并表明所有$ n $ d量子液体构成$*$ - 凝结完整的更高类别，可以从简单的coslice 1类别中明确计算其等效类型。
We develop a mathematical theory of separable higher categories based on Gaiotto and Johnson-Freyd's work on condensation completion. Based on this theory, we prove some fundamental results on $E_m$-multi-fusion higher categories and their higher centers. We also outline a theory of unitary higher categories based on a $*$-version of condensation completion. After these mathematical preparations, based on the idea of topological Wick rotation, we develop a unified mathematical theory of all quantum liquids, which include topological orders, SPT/SET orders, symmetry-breaking orders and CFT-like gapless phases. We explain that a quantum liquid consists of two parts, the topological skeleton and the local quantum symmetry, and show that all $n$D quantum liquids form a $*$-condensation complete higher category whose equivalence type can be computed explicitly from a simple coslice 1-category.
