Topological defects of 2+1D systems from line excitations in 3+1D bulk

• URL: http://arxiv.org/abs/2407.02488v1
• Date: Tue, 2 Jul 2024 17:59:48 GMT
• Title: Topological defects of 2+1D systems from line excitations in 3+1D bulk
• Authors: Wenjie Ji, Xie Chen,
• Abstract summary: In 2+1D topological phases, a direct correspondence can exist between anyonic excitations in the bulk and the topological point defects/primary fields in the boundary 1+1D conformal field theory. We study how line excitations in 3+1D topological phases become line defects in the boundary 2+1D theory using the Topological Holography/Symmetry Topological Field Theory framework.
• Score: 2.8892315355773612
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The bulk-boundary correspondence of topological phases suggests strong connections between the topological features in a d+1-dimensional bulk and the potentially gapless theory on the (d-1)+1-dimensional boundary. In 2+1D topological phases, a direct correspondence can exist between anyonic excitations in the bulk and the topological point defects/primary fields in the boundary 1+1D conformal field theory. In this paper, we study how line excitations in 3+1D topological phases become line defects in the boundary 2+1D theory using the Topological Holography/Symmetry Topological Field Theory framework. We emphasize the importance of "descendent" line excitations and demonstrate in particular the effect of the Majorana chain defect: it leads to a distinct loop condensed gapped boundary state of the 3+1D fermionic Z2 topological order, and leaves signatures in the 2+1D Majorana-cone critical theory that describes the transition between the two types of loop condensed boundaries. Effects of non-invertible line excitations, such as Cheshire strings, are also discussed in bosonic 3+1D topological phases and the corresponding 2+1D critical points.

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