Orbifold completion of defect bicategories

By Nils Carqueville, Ingo Runkel. 2012

141 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3a91045592163de081aa55f32e65909fdb6ebf8f

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Citations in the corpus

Fusion 2-categories and a state-sum invariant for 4-manifolds (2018, result): “This corollary is analogous to a result of Carqueville–Runkel [CR16], who show that replacing a 2-category by the 2-category of internal separable Frobenius algebras is an idempotent operation.”
On finite symmetries and their gauging in two dimensions (2017, methodology): “We recommend to the readers textbooks by Bischoff, Longo, Kawahigashi and Rehren [6] and Etingof, Gelaki, Nikshych and Ostrik [7] from the first two communities and the articles by Carqueville and Runkel [8] and by Brunner, Carqueville and Plencner [9] from the third community as the starting points”
Higher Gauging and Non-invertible Condensation Defects (2022, unknown): “This has been discussed extensively for non-invertible 0-form symmetries in 1+1d [35,39,40,3,15,14,41] and for non-invertible 1-form symmetries in 2+1d (see [42–45] for recent discussions).”
Q-system completion for C⁎ 2-categories (2021, unknown): “Given a C ∗ / W ∗ 2-category C , its Q-system completion is the 2-category QSys ( C ) of Q-systems, bimodules, and intertwiners in C , which has been studied previously in [NY16, BKLR15, GY20], building on algebraic versions in [Yam04a, CR16, DR18, GJF19].”
On gauging finite subgroups (2017, unknown): “[17–21].”