A Geometric Approach to Boundaries and Surface Defects in Dijkgraaf–Witten Theories

Dijkgraaf–Witten theories are extended three-dimensional topological field theories of Turaev–Viro type. They can be constructed geometrically from categories of bundles via linearization. Boundaries and surface defects or interfaces in quantum field theories are of interest in various applications and provide structural insight. We perform a geometric study of boundary conditions and surface defects in Dijkgraaf–Witten theories. A crucial tool is the linearization of categories of relative bundles. We present the categories of generalized Wilson lines produced by such a linearization procedure. We establish that they agree with the Wilson line categories that are predicted by the general formalism for boundary conditions and surface defects in three-dimensional topological field theories that has been developed in Fuchs et al. (Commun Math Phys 321:543–575, 2013 )