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Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries
by Siyuan Wang, Yanyan Chen, Hongyu Wang, Yuting Hu, Yidun Wan
Submission summary
| Authors (as registered SciPost users): | Siyuan Wang |
| Submission information | |
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| Preprint Link: | scipost_202406_00062v1 (pdf) |
| Date submitted: | 2024-06-28 14:04 |
| Submitted by: | Wang, Siyuan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this paper, we apply the method of Fourier transform and basis rewriting developed in [JHEP02(2020)030] for the two-dimensional quantum double model of topological orders to the three-dimensional gauge theory model (with a gauge group G) of three-dimensional topological orders. We find that the gapped boundary condition of the gauge theory model is characterized by a Frobenius algebra in the representation category Rep(G) of G, which also describes the charge splitting and condensation on the boundary. We also show that our Fourier transform maps the three-dimensional gauge theory model with input data G to the Walker-Wang model with input data Rep(G) on a trivalent lattice with dangling edges, after truncating the Hilbert space by projecting all dangling edges to the trivial representation of G. This Fourier transform also provides a systematic construction of the gapped boundary theory of the Walker-Wang model. This establishes a correspondence between two types of topological field theories: the extended Dijkgraaf-Witten and extended Crane-Yetter theories.
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