Orbifolds of n–dimensional defectTQFTs

We introduce the notion of [math] –dimensional topological quantum field theory (TQFT) with defects as a symmetric monoidal functor on decorated stratified bordisms of dimension [math] . The familiar closed or open–closed TQFTs are special cases of defect TQFTs, and for [math] and [math] our general definition recovers what had previously been studied in the literature.¶ Our main construction is that of “generalised orbifolds” for any [math] –dimensional defect TQFT: Given a defect TQFT [math] , one obtains a new TQFT [math] by decorating the Poincaré duals of triangulated bordisms with certain algebraic data [math] and then evaluating with [math] . The orbifold datum [math] is constrained by demanding invariance under [math] –dimensional Pachner moves. This procedure generalises both state sum models and gauging of finite symmetry groups for any [math] . After developing the general theory, we focus on the case [math] .