Orbifold completion of defect bicategories
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Publication:260206
DOI10.4171/QT/76zbMATH Open1360.18007arXiv1210.6363OpenAlexW3104528426MaRDI QIDQ260206
Author name not available (Why is that?)
Publication date: 18 March 2016
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1210.6363
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