期刊
QUANTUM TOPOLOGY
卷 7, 期 2, 页码 203-279出版社
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/QT/76
关键词
Pivotal bicategories; TQFT; matrix factorisations
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 of B-orb and (Borb)(orb) S congruent to 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.
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