TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.14.4.065
TI  - Codimension-2 defects and higher symmetries in (3+1)D topological phases
PY  - 2023/04/11
UR  - https://scipost.org/SciPostPhys.14.4.065
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 14
IS  - 4
SP  - 065
A1  - Barkeshli, Maissam
AU  - Chen, Yu-An
AU  - Huang, Sheng-Jie
AU  - Kobayashi, Ryohei
AU  - Tantivasadakarn, Nathanan
AU  - Zhu, Guanyu
AB  - (3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error-correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of $\mathbb{Z}_2$ gauge theory with fermionic charges, in $\mathbb{Z}_2 \times \mathbb{Z}_2$ gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral ($D_n$) and alternating ($A_6$) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an $H^4$ cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of the interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D $A_6$ gauge theory.
ER  -

@Article{10.21468/SciPostPhys.14.4.065,
	title={{Codimension-2 defects and higher symmetries in (3+1)D topological phases}},
	author={Maissam Barkeshli and Yu-An Chen and Sheng-Jie Huang and Ryohei Kobayashi and Nathanan Tantivasadakarn and Guanyu Zhu},
	journal={SciPost Phys.},
	volume={14},
	pages={065},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.14.4.065},
	url={https://scipost.org/10.21468/SciPostPhys.14.4.065},
}