Line and surface defects in Reshetikhin-Turaev TQFT

Abstract

A modular tensor category $\mathcal{C}$ gives rise to a Reshetikhin-Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded $\mathcal{C}$-coloured ribbon graphs. We extend this construction to include bordisms with surface defects which in turn can meet along line defects. The surface defects are labelled by $\Delta$-separable symmetric Frobenius algebras and the line defects by "multi-modules" which are equivariant with respect to a cyclic group action. Our invariant cannot distinguish non-isotopic embeddings of 2-spheres, but we give an example where it distinguishes non-isotopic embeddings of 2-tori.

38 pages; v2: minor corrections and improvements

References in corpus (7)

• Genons, twist defects, and projective non-Abelian braiding statistics
• Orbifolds of n-dimensional defect TQFTs
• 3-dimensional defect TQFTs and their tricategories
• The ${\mathfrak{sl}}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality
• Lecture notes on 2-dimensional defect TQFT
• Topological orders and factorization homology
• Orbifolds of Reshetikhin-Turaev TQFTs

Cited by in corpus (19)

• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• On lattice models of gapped phases with fusion category symmetries
• Decomposition, condensation defects, and fusion
• Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond
• Higher categorical symmetries and gauging in two-dimensional spin systems
• Orbifolds of n-dimensional defect TQFTs
• Fermionization of fusion category symmetries in 1+1 dimensions
• Parity and Spin CFT with boundaries and defects
• Orbifolds of Reshetikhin-Turaev TQFTs
• Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part I
• Topological defects
• Condensations in higher categories
• Domain walls between 3d phases of Reshetikhin-Turaev TQFTs
• Reshetikhin-Turaev TQFTs close under generalised orbifolds
• Weak Hopf tube algebra for domain walls between 2d gapped phases of Turaev-Viro TQFTs
• Orbifold graph TQFTs
• Operator lift of Reshetikhin-Turaev formalism to Khovanov-Rozansky TQFTs
• Orbifold completion of 3-categories
• A geometrical description of untwisted 3d Dijkgraaf-Witten TQFT with defects