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 [1] 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.

中文翻译：

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陈-西蒙斯理论的接口和扩展希尔伯特空间

物质的 (2 + 1) 维拓扑相的低能量有效场理论为研究基态中的纠缠提供了有力的途径。在 [1] 中，通过配备一组拓扑边界条件 (TBC) 的阿贝尔陈 - 西蒙斯理论研究了不同阿贝尔拓扑相之间的纠缠。在本文中，我们将 TBC 的概念扩展到非阿贝尔陈 - 西蒙斯理论，为跨非阿贝尔拓扑相的一类有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，并允许直接在规范理论中计算纠缠。因为我们允许简单的接口，这包括在黎曼曲面上量化的任何（紧凑）陈 - 西蒙斯理论中扩展希尔伯特空间的通用构造。此外，这为沿有隙界面粘合的物质有隙相的有效基态的希尔伯特空间提供了建设性和原则性的定义。最后，我们描述了手术的广义概念，将拓扑场论中的强大工具添加到间隙界面工具箱中。