Orbifold completion of defect bicategories (Q260206)

The paper under review provides a new perspective on the orbifolding procedure for 2-dimensional topological quantum field theories (TFTs) with defects.NEWLINENEWLINEA TFT with defects is a generalization of the usual notion of a symmetric monoidal functor out of a bordism category, where bordisms and their boundaries are decorated with phases and domain walls or defect conditions. One of the simplest examples recovers the notion of open/closed TFTs. A 2-dimensional oriented TFT with defects \(\tau\) gives rise to a certain pivotal bicategory \(\mathcal D_\tau\) of ``worldsheet phases'', in terms of which the orbifolded TFT \(\tau^{\mathrm{orb}}\) is constructed.NEWLINENEWLINEThe core of the paper consists of two purely categorical constructions, called equivariant completion and orbifold completion, which apply in particular to \(\mathcal D_\tau\), but also, more generally, to any pivotal bicategory with idempotent complete 1-morphism categories; they are certain categories of separable (respectively symmetric and separable) Frobenius algebras, bimodules, and bimodule maps. Thus, these completion constructions insert the above story into a broader perspective.NEWLINENEWLINEIn the last part of the paper, the authors apply their formalism to Landau-Ginzburg models, showing how the usual notion of orbifold fits into it. This includes a proof of Knörrer periodicity.