Orbifold completion of defect bicategories

  • Nils Carqueville

    Universität Wien, Austria
  • Ingo Runkel

    Universität Hamburg, Germany


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 B\mathcal B as input and returns its "orbifold completion" Borb\mathcal B_{\mathrm {orb}}. The completion satisfies the natural properties BBorb\mathcal B \subset \mathcal B_{\mathrm {orb}} and (Borb)orbBorb(\mathcal B_{\mathrm {orb}})_{\mathrm{orb}} \cong \mathcal B_{\mathrm {orb}}, and it gives rise to various new equivalences and nondegeneracy results. When applied to TFTs, the objects in Borb\mathcal B_{\mathrm {orb}} correspond to generalised orbifolds of the theories in B\mathcal 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 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