Codimension2 defects and higher symmetries in (3+1)D topological phases
Abstract
(3+1)D topological phases of matter can host a broad class of nontrivial topological defects of codimension1, 2, and 3, of which the wellknown 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 faulttolerant logical operations in topological quantum errorcorrecting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension2 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&Z;2 gauge theory with fermionic charges, in \mathbb{Z}_2 \times \mathbb{Z}_2&Z;2×&Z;2 gauge theory with bosonic charges, and also in nonAbelian discrete gauge theories based on dihedral (D_nDn) and alternating (A_6A6) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H^4H4 cohomology class that characterizes part of an underlying 3group symmetry of the topological order. The equations involving background gauge fields for the 3group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with nonAbelian flux loops (defining part of a noninvertible higher symmetry), examples of noninvertible codimension2 defects, and examples of the interplay of codimension2 defects with codimension1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D A_6A6 gauge theory.
 Publication:

SciPost Physics
 Pub Date:
 April 2023
 DOI:
 10.21468/SciPostPhys.14.4.065
 arXiv:
 arXiv:2208.07367
 Bibcode:
 2023ScPP...14...65B
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Quantum Algebra;
 Quantum Physics
 EPrint:
 70 pages, 42 figures