



02685nas a2200253   4500008004100000245007700041210006900118260001400187520182700201653002102028653002702049653004202076653003502118653003002153653003102183653005202214100002302266700001602289700002102305700002202326700003002348700001602378856003702394       2022                        eng d00aCodimension-2 defects and higher symmetries in (3+1)D topological phases0 aCodimension2 defects and higher symmetries in 31D topological ph  c8/15/20223 a<p>(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 Z2 gauge theory with fermionic charges, in Z2&times;Z2 gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral (Dn) and alternating (A6) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H4 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 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 A6 gauge theory.</p>10aFOS: Mathematics10aFOS: Physical sciences10aHigh Energy Physics - Theory (hep-th)10aMathematical Physics (math-ph)10aQuantum Algebra (math.QA)10aQuantum Physics (quant-ph)10aStrongly Correlated Electrons (cond-mat.str-el)1 aBarkeshli, Maissam1 aChen, Yu-An1 aHuang, Sheng-Jie1 aKobayashi, Ryohei1 aTantivasadakarn, Nathanan1 aZhu, Guanyu  uhttps://arxiv.org/abs/2208.07367