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

TL;DR

This paper explores how line excitations in 3+1D topological phases manifest as line defects in 2+1D boundary theories, revealing new boundary states and critical phenomena through topological holography.

Contribution

It introduces a framework connecting 3+1D line excitations to 2+1D boundary defects, highlighting the role of descendent excitations and non-invertible lines in topological phases.

Findings

Majorana chain defect induces a distinct gapped boundary state

Signatures of line excitations appear in 2+1D critical theories

Cheshire strings influence boundary critical points

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.