标题： 1+1D无能隙对称保护相的分类通过拓扑全息理论 显示英文标题

标题： Classification of 1+1D gapless symmetry protected phases via topological holography

摘要： 对具有全局对称性的系统与高维拓扑场理论之间的全息对应关系由对称性拓扑场理论（SymTFT）给出。在此框架中，时空维度1+1D中绝缘相的分类对应于通过凝聚任意子来约束SymTFT的机制的分类。在本工作中，我们将这些结果扩展到表征无能隙对称保护拓扑态：表现出由对称性和拓扑保护的边缘模的对称丰富无能隙相或临界点。我们建立了1+1D玻色型gSPT与2+1D SymTFT的部分约束边界之间的一一对应关系。从一般的物理考虑出发，我们确定了定义1+1D gSPT所需的数据和一致性条件，并表明这些数据精确匹配2+1D量子双模型的对称性保持部分约束（或部分闭合边界）的数据。我们通过维度约简（薄板）构造来说明这一对应关系，这使得从SymTFT的角度直观推导出gSPT的性质，如边缘模、出现的异常以及对扰动的稳定性成为可能。确定定义1+1D gSPT所需的条件，并表明它们完全决定了gSPT的物理性质，包括边缘模和出现的异常。 显示英文摘要

摘要： Symmetry topological field theory (SymTFT) gives a holographic correspondence between systems with a global symmetry and a higher-dimensional topological field theory. In this framework, classification of gapped phases of matter in spacetime dimension 1+1D correspond to classifications of mechanisms to confine the SymTFT by condensing anyons. In this work, we extend these results to characterize gapless symmetry-protected topological states: symmetry-enriched gapless phases or critical points that exhibit edge modes protected by symmetry and topology. We establish a one-to-one correspondence between 1+1D bosonic gSPTs, and partially-confined boundaries of 2+1D SymTFTs. From general physical considerations, we determine the set of data and consistency conditions required to define a 1+1D gSPT, and show that this data precisely matches that of symmetry-preserving partial confinement (or partially gapped boundaries) of 2+1D quantum double models. We illustrate this correspondence through a dimensional reduction (thin-slab) construction, which enables a physically-intuitive derivation of how properties of the gSPT such as edge modes, emergent anomalies, and stability to perturbations arise from the SymTFT perspective.ditions required to define a 1+1D gSPT and show that they fully determine the physics of the gSPT including edge modes and emergent anomaly.