Cheshire charge in (3+1)-dimensional topological phases

The authors examine the phenomenon of ``Cheshire charge'' in topological phases of matter in three spatial dimensions. A looplike excitation is said to carry Cheshire charge if the charge is not locally detectable, that is, it can only be observed by a nonlocal process such as shrinking the loop to a point. The authors show that ``Cheshire charge'' is a generic feature of three-dimensional topological phases. They relate it to other features of these phases, such as three-loop braiding, as well as to higher-category theory that is hypothesized to be the general mathematical framework describing three-dimensional topological phases.