Orbifold completion of defect bicategories

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 "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.

62 pages; v2: minor improvements; v3: expanded discussion of adjoints in equivariant completion, minor changes; v4=journal version: improved and at times more detailed exposition, new Example 4.6 (due to anonymous referee)

Cited by in corpus (65)

• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• On finite symmetries and their gauging in two dimensions
• On gauging finite subgroups
• Kramers-Wannier-like duality defects in (3+1)d gauge theories
• Non-Invertible Duality Defects in 3+1 Dimensions
• Symmetries and Strings of Adjoint QCD${}_2$
• Higher Gauging and Non-invertible Condensation Defects
• Orbifold groupoids
• Non-Invertible Higher-Categorical Symmetries
• Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
• Notes on generalized global symmetries in QFT
• Asymptotic density of states in 2d CFTs with non-invertible symmetries
• Construction of two-dimensional topological field theories with non-invertible symmetries
• Branes and Non-Invertible Symmetries
• Non-invertible Symmetries of Class $\mathcal{S}$ Theories
• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
• Non-invertible Symmetries and Higher Representation Theory I
• On lattice models of gapped phases with fusion category symmetries
• Obstructions to Gapped Phases from Non-Invertible Symmetries
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Bootstrapping Non-Invertible Symmetries
• Non-invertible Symmetries and Higher Representation Theory II
• Numerical evidence for a Haagerup conformal field theory
• Anomalies of Non-Invertible Symmetries in (3+1)d
• Orbifolds of n-dimensional defect TQFTs
• Topological field theories and symmetry protected topological phases with fusion category symmetries
• Duality Defects in $E_8$
• 3-dimensional defect TQFTs and their tricategories
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• Lorentzian Dynamics and Factorization Beyond Rationality
• Categories of quantum liquids I
• A quasi-Hopf algebra for the triplet vertex operator algebra
• Topological Field Theory with Haagerup Symmetry
• Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases
• Comments on Non-invertible Symmetries in Argyres-Douglas Theories
• The Morita theory of quantum graph isomorphisms
• Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal Field Theory
• Fermionization of fusion category symmetries in 1+1 dimensions
• Fermionization and boundary states in 1+1 dimensions
• Q-system completion for C* 2-categories
• Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains
• Parity and Spin CFT with boundaries and defects
• Composing topological domain walls and anyon mobility
• Decomposition, Trivially-Acting Symmetries, and Topological Operators
• The holography of non-invertible self-duality symmetries
• Orbifolds by 2-groups and decomposition
• Topological defects
• Gauging non-invertible symmetries on the lattice
• A fresh view on string orbifolds
• Realizing IR theories by projections in the UV
• Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
• Global symmetries of quantum lattice models under non-invertible dualities
• Phase transitions in GLSMs and defects
• Complementary Projection Defects and Decompositions
• Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders
• Generalized Landau Paradigm for quantum phases and phase transitions
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• From gauging to duality in one-dimensional quantum lattice models
• Condensation Completion and Defects in 2+1D Topological Orders
• Fusion of interfaces in Landau-Ginzburg models: a functorial approach
• Orbifold completion of 3-categories
• Truncated affine Rozansky--Witten models as extended defect TQFTs