Orbifold completion of defect bicategories

  • Nils Carqueville

    Universität Wien, Austria
  • Ingo Runkel

    Universität Hamburg, Germany

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 "world sheet phases" and defects between them. We develop a general framework which takes such a bicategory as input and returns its "orbifold completion" . The completion satisfies the natural properties and , and it gives rise to various new equivalences and nondegeneracy results. When applied to TFTs, the objects in correspond to generalised orbifolds of the theories in . 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 this article

Nils Carqueville, Ingo Runkel, Orbifold completion of defect bicategories. Quantum Topol. 7 (2016), no. 2, pp. 203–279

DOI 10.4171/QT/76