Orbifold completion of defect bicategories
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.
Cite
@article{arxiv.1210.6363,
title = {Orbifold completion of defect bicategories},
author = {Nils Carqueville and Ingo Runkel},
journal= {arXiv preprint arXiv:1210.6363},
year = {2016}
}
Comments
62 pages; v2: minor improvements; v3: expanded discussion of adjoints in equivariant completion, minor changes; v4=journal version: improved and at times more detailed exposition, new Example 4.6 (due to anonymous referee)