Orbifold completion of defect bicategories

TL;DR

This paper develops a framework for orbifold completion of defect bicategories in topological field theories, enabling the construction of generalized orbifolds and revealing new equivalences and properties.

Contribution

It introduces a general method to obtain orbifold completions of defect bicategories, extending the orbifolding procedure in topological quantum field theories.

Findings

Constructed orbifold completions satisfying natural properties.

Unified and generalized conventional orbifolds in Landau-Ginzburg models.

Identified new orbifold equivalences and nondegeneracy results.

Abstract

Orbifolds of two-dimensional quantum field theories have a natural formulation in terms of defects or domain walls. This perspective allows for a rich generalisation of the orbifolding procedure, which we study in detail for the case of topological field theories. Namely, a TFT with defects gives rise to a pivotal bicategory of "worldsheet phases" and defects between them. We develop a general framework which takes such a bicategory B as input and returns its "orbifold completion" B_orb. The completion satisfies the natural properties B \subset B_orb and (B_orb)_orb = B_orb, and it gives rise to various new equivalences and nondegeneracy results. When applied to TFTs, the objects in B_orb correspond to generalised orbifolds of the theories in B. In the example of Landau-Ginzburg models we recover and unify conventional equivariant matrix factorisations, prove when and how (generalised) orbifolds again produce open/closed TFTs, and give nontrivial examples of new orbifold equivalences.