2023/06/23 by Siyuan Wang, Wang, Siyuan, Yanyan Chen +7
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2306.13530
openalex publication_date 2023/06/23 · openalex created_date 2023/06/27 · openalex updated_date 2026/07/28
In this paper, we apply the method of Fourier transform and basis rewriting developed in arXiv:1910.13441 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 \mathcal 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 \mathcal 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.