Orbifolds of n-dimensional defect TQFTs

Abstract

We introduce the notion of $n$-dimensional topological quantum field theory (TQFT) with defects as a symmetric monoidal functor on decorated stratified bordisms of dimension $n$. The familiar closed or open-closed TQFTs are special cases of defect TQFTs, and for $n=2$ and $n=3$ our general definition recovers what had previously been studied in the literature. Our main construction is that of "generalised orbifolds" for any $n$-dimensional defect TQFT: Given a defect TQFT $\mathcal{Z}$, one obtains a new TQFT ${\mathcal{Z}}_{\mathcal{A}}$ by decorating the Poincaré duals of triangulated bordisms with certain algebraic data $\mathcal{A}$ and then evaluating with $\mathcal{Z}$. The orbifold datum $\mathcal{A}$ is constrained by demanding invariance under $n$-dimensional Pachner moves. This procedure generalises both state sum models and gauging of finite symmetry groups, for any $n$. After developing the general theory, we focus on the case $n=3$.

arXiv comment79 pages; v2: modified definition of stratified bordism category; v3: minor corrections and modifications

References in corpus (25)

• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Models for gapped boundaries and domain walls
• Genons, twist defects, and projective non-Abelian braiding statistics
• TFT construction of RCFT correlators III: Simple currents
• Spherical Categories
• Defect lines, dualities, and generalised orbifolds
• Bicategories for boundary conditions and for surface defects in 3-d TFT
• Orbifold completion of defect bicategories
• Lattice Topological Field Theory in Two Dimensions
• On Gauging Symmetry of Modular Categories
• Turaev-Viro invariants as an extended TQFT
• Higher Frobenius-Schur Indicators for Pivotal Categories
• Three-dimensional topological field theory and symplectic algebraic geometry I
• Discrete torsion defects
• 3-dimensional defect TQFTs and their tricategories
• The blob complex
• Line and surface defects in Reshetikhin-Turaev TQFT
• Topological Models on the Lattice and a Remark on String Theory Cloning
• Orbifold equivalent potentials
• On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories
• Lecture notes on 2-dimensional defect TQFT
• Orbifolds of Reshetikhin-Turaev TQFTs
• Gray categories with duals and their diagrams
• A note on permutation twist defects in topological bilayer phases
• Calabi-Yau completions and orbifold equivalences

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