论文标题
界面和Chern-Simons理论的扩展希尔伯特空间
Interfaces and the extended Hilbert space of Chern-Simons theory
论文作者
论文摘要
$（2+1）$尺寸拓扑阶段的低能源有效现场理论为调查其基础状态的纠缠提供了强大的途径。在\ cite {Fliss：2017wop}通过配备了一组拓扑边界条件（TBC）的Abelian Chern-Simons理论研究了不同Abelian拓扑阶段之间的纠缠。在本文中，我们将TBC的概念扩展到了非亚洲Chern-Simons的理论，为在非亚伯利亚拓扑阶段的一类间隙界面提供了有效的描述。这些边界条件为量子理论的扩展希尔伯特空间提供了定义关系，并允许直接在仪表理论中计算纠缠。因为我们允许微不足道的接口，所以这包括在任何（紧凑的）Chern-Simons理论中量化在Riemann表面上的（紧凑的）Chern-Simons理论的通用结构。此外，这为希尔伯特（Hilbert）空间提供了一个建设性和原则性的定义，该空间是沿着缝隙界面粘合物质的间隙阶段的有效基态。最后，我们描述了一个广义的手术概念，从拓扑字段理论到缝隙界面工具箱增加了一个强大的工具。
The low energy effective field theories of $(2+1)$ dimensional topological phases of matter provide powerful avenues for investigating entanglement in their ground states. In \cite{Fliss:2017wop} the entanglement between distinct Abelian topological phases was investigated through Abelian Chern-Simons theories equipped with a set of topological boundary conditions (TBCs). In the present paper we extend the notion of a TBC to non-Abelian Chern-Simons theories, providing an effective description for a class of gapped interfaces across non-Abelian topological phases. These boundary conditions furnish a defining relation for the extended Hilbert space of the quantum theory and allow the calculation of entanglement directly in the gauge theory. Because we allow for trivial interfaces, this includes a generic construction of the extended Hilbert space in any (compact) Chern-Simons theory quantized on a Riemann surface. Additionally, this provides a constructive and principled definition for the Hilbert space of effective ground states of gapped phases of matter glued along gapped interfaces. Lastly, we describe a generalized notion of surgery, adding a powerful tool from topological field theory to the gapped interface toolbox.
