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- W4308503296 abstract "2+1d topological phases are well characterized by the fusion rules and braiding/exchange statistics of fractional point excitations. In 4+1d, some topological phases contain only fractional loop excitations. What kind of loop statistics exist? We study the 4+1d gauge theory with 2-form $mathbb{Z}_2$ gauge field (the loop only toric code) and find that while braiding statistics between two different types of loops can be nontrivial, the self `exchange' statistics are all trivial. In particular, we show that the electric, magnetic, and dyonic loop excitations in the 4+1d toric code are not distinguished by their self-statistics. They tunnel into each other across 3+1d invertible domain walls which in turn give explicit unitary circuits that map the loop excitations into each other. The $SL(2,mathbb{Z}_2)$ symmetry that permutes the loops, however, cannot be consistently gauged and we discuss the associated obstruction in the process. Moreover, we discuss a gapless boundary condition dubbed the `fractional Maxwell theory' and show how it can be Higgsed into gapped boundary conditions. We also discuss the generalization of these results from the $mathbb{Z}_2$ gauge group to $mathbb{Z}_N$." @default.
- W4308503296 created "2022-11-12" @default.
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- W4308503296 date "2021-12-03" @default.
- W4308503296 modified "2023-09-23" @default.
- W4308503296 title "Loops in 4+1d Topological Phases" @default.
- W4308503296 doi "https://doi.org/10.48550/arxiv.2112.02137" @default.
- W4308503296 hasPublicationYear "2021" @default.
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