TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.1.018
TI  - Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries
PY  - 2025/07/17
UR  - https://scipost.org/SciPostPhys.19.1.018
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 1
SP  - 018
A1  - Wang, Siyuan
AU  - Chen, Yanyan
AU  - Wang, Hongyu
AU  - Hu, Yuting
AU  - Wan, Yidun
AB  - In this paper, we apply the method of Fourier transform and basis rewriting developed in [H. Wang et al., J. High Energy Phys. 02, 030 (2020)] 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 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.
ER  -

@Article{10.21468/SciPostPhys.19.1.018,
	title={{Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries}},
	author={Siyuan Wang and Yanyan Chen and Hongyu Wang and Yuting Hu and Yidun Wan},
	journal={SciPost Phys.},
	volume={19},
	pages={018},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.1.018},
	url={https://scipost.org/10.21468/SciPostPhys.19.1.018},
}