- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:39
Quantum Topology
Quantum Topol.
QT
1663-487X
1664-073X
General
10.4171/QT
http://www.ems-ph.org/doi/10.4171/QT
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
7
2016
2
Orbifold completion of defect bicategories
Nils
Carqueville
Universität Wien, WIEN, AUSTRIA
Ingo
Runkel
Universität Hamburg, HAMBURG, GERMANY
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 "world sheet phases" and defects between them. We develop a general framework which takes such a bicategory $\mathcal B$ as input and returns its "orbifold completion" $\mathcal B_{\mathrm {orb}}$. The completion satisfies the natural properties $\mathcal B \subset \mathcal B_{\mathrm {orb}}$ and $(\mathcal B_{\mathrm {orb}})_{\mathrm{orb}} \cong \mathcal B_{\mathrm {orb}}$, and it gives rise to various new equivalences and nondegeneracy results. When applied to TFTs, the objects in $\mathcal B_{\mathrm {orb}}$ correspond to generalised orbifolds of the theories in $\mathcal B$. 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.
Category theory; homological algebra
General
Manifolds and cell complexes
203
279
10.4171/QT/76
http://www.ems-ph.org/doi/10.4171/QT/76