Orbifolds of n-dimensional defect TQFTs

Understand

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 $\mathcal{Z}$, one obtains a new TQFT $\mathcal{Z}_{\mathcal{A}}$ by decorating the Poincar\'e duals of triangulated bordisms with certain algebraic data $\mathcal{A}$ and then evaluating with $\mathcal{Z}$.
• The orbifold datum $\mathcal{A}$ is constrained by demanding invariance under $n$-dimensional Pachner moves.