Orbifolds of n-dimensional defect TQFTs

We introduce the notion of n -dimensional topological quantum field theory (TQFT) with defects as a symmetric monoidal functor on decorated stratified bordisms of dimension n. The familiar closed or open-closed TQFTs are special cases of defect TQFTs, and for n = 2 and n = 3 our general definition recovers what had previously been studied in the literature. Our main construction is that of "generalised orbifolds" for any n -dimensional defect TQFT: Given a defect TQFT Z, one obtains a new TQFT Z(A) by decorating the Poincare duals of triangulated bordisms with certain algebraic data A and then evaluating with Z. The orbifold datum A is constrained by demanding invariance under n -dimensional Pachner moves. This procedure generalises both state sum models and gauging of finite symmetry groups for any n. After developing the general theory, we focus on the case n = 3.