Compatible braidings with Hopf links, multi-loop, and Borromean rings in $(3+1)$-dimensional spacetime

Understand

Braiding phases among topological excitations are key data for physically characterizing topological orders.

• In this paper, we provide a field-theoretical approach towards a complete list of mutually compatible braiding phases of topological orders in (3+1)D spacetime.
• More concretely, considering a discrete gauge group as input data, topological excitations in this paper are bosonic \particles carrying gauge charges and loops carrying gauge fluxes.
• Among these excitations, there are three classes of root braiding processes: particle-loop braidings (i.e., the familiar Aharonov-Bohm phase of winding an electric charge around a thin magnetic solenoid), multi-loop braidings [Phys.