紧致自由玻色子的边界：通过边缘模与边界SymTFT
Boundaries of the compact free boson through edge modes and boundary SymTFT
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中文总结 AI 辅助
本研究通过耦合体标量场与拓扑边缘模，系统分类了紧致自由玻色子的边界条件，并在边界SymTFT框架下揭示了Dirichlet与Neumann边界的数据结构及T-对偶关系，同时扩展到非紧致模和多场情形。
中文摘要 AI 辅助
我们通过将体标量场与一维拓扑边缘模耦合，研究了紧致自由玻色子理论的边界条件。我们证明，单个紧致边缘模实现了Dirichlet族，而双场系统实现了Neumann族；更一般的紧致边缘理论可以描述边界条件的叠加，并重现预期的边界算子谱。然后，我们在边界SymTFT框架下研究该系统。我们证明，Dirichlet和Neumann边界的边缘模理论编码在边界SymTFT角上的局域自由度以及拓扑面上的极化选择中。我们进一步证明，T-对偶缺陷交换与Dirichlet和Neumann构型相关的数据。最后，我们探索涉及非紧致边缘模和多体标量场的扩展，分别获得连续边界谱和混合边界条件。
英文摘要
We study boundary conditions of the compact free boson theory by coupling the bulk scalar to one-dimensional topological edge modes. We show that a single compact edge mode realizes the Dirichlet family, while a two field system realizes the Neumann family; more general compact edge theories can describe superpositions of boundary conditions and reproduce the expected boundary operator spectra. We then study this system in the framework of boundary SymTFT. We show that the edge mode theories of Dirichlet and Neumann boundaries are encoded in the degrees of freedom localized on the corners and the choice of polarization on the topological face of the boundary SymTFT. We further show that the T-duality defect exchanges the data associated with the Dirichlet and Neumann configurations. Finally, we explore extensions involving non-compact edge modes and multiple bulk fields, obtaining continuous boundary spectra in the first case and mixed boundary conditions in the second.
发表机构
- University at Albany（奥尔巴尼大学）
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