Fermionic modular categories and the 16-fold way

DOI10.1063/1.4982048zbMath1365.81098arXiv1603.09294OpenAlexW2322806343MaRDI QIDQ2981023

Julia Yael Plavnik, Siu-Hung Ng, Zhenghan Wang, César Galindo, Paul Bruillard, Eric C. Rowell, Tobias Hagge

Publication date: 8 May 2017

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.09294

Mathematics Subject Classification ID

Many-body theory; quantum Hall effect (81V70) Topological field theories in quantum mechanics (81T45) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Transcendence theory of Drinfel'd and (t)-modules (11J93) Modular spaces (46A80)

Related Items

Cohomology of finite tensor categories: Duality and Drinfeld centers ⋮ From gauge to higher gauge models of topological phases ⋮ Classification of metaplectic modular categories ⋮ Slightly Degenerate Categories and ℤ-Modular Data ⋮ Tetrahedral symmetry of \(6j\)-symbols in fusion categories ⋮ M-theoretic genesis of topological phases ⋮ \( \mathrm{SL}(2,\mathbb{Z})\) action on QFTs with \(\mathbb{Z}_2\) symmetry and the Brown-Kervaire invariants ⋮ Operator algebras in rigid \(\mathrm{C}^\ast\)-tensor categories ⋮ On slightly degenerate fusion categories ⋮ Semisimple four‐dimensional topological field theories cannot detect exotic smooth structure ⋮ Minimal nondegenerate extensions ⋮ Classification of super-modular categories by rank ⋮ Hecke relations among 2d fermionic RCFTs ⋮ Modular quasi-Hopf algebras and groups with one involution ⋮ When does a three-dimensional Chern-Simons-Witten theory have a time reversal symmetry? ⋮ On the minimal extension and structure of braided weakly group-theoretical fusion categories ⋮ Drinfeld centers of fusion categories arising from generalized Haagerup subfactors ⋮ Anomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTs ⋮ Unnamed Item ⋮ Structure, examples and classification for generalized near-group fusion categories ⋮ Infinite families of potential modular data related to quadratic categories ⋮ Metaplectic categories, gauging and property \(F\) ⋮ \(U(1)\) spin Chern-Simons theory and Arf invariants in two dimensions ⋮ The symmetric tensor product on the Drinfeld centre of a symmetric fusion category ⋮ Vertex operator superalgebras and the 16-fold way ⋮ Classification of topological phases with finite internal symmetries in all dimensions ⋮ Symmetries and strings of adjoint \(\mathrm{QCD}_2\) ⋮ Congruence subgroups and super-modular categories ⋮ Braided zesting and its applications ⋮ Braided Picard groups and graded extensions of braided tensor categories ⋮ Topological field theories and symmetry protected topological phases with fusion category symmetries ⋮ Mathematics of topological quantum computing ⋮ Fermion condensation and super pivotal categories ⋮ On classification of super-modular categories of rank 8 ⋮ Deligne categories in lattice models and quantum field theory, \textit{or} making sense of O(N) symmetry with non-integer N ⋮ Bootstrapping fermionic rational CFTs with three characters ⋮ Computing the group of minimal non-degenerate extensions of a super-Tannakian category ⋮ Numerical identification and gapped boundaries of Abelian fermionic topological order ⋮ On finite non-degenerate braided tensor categories with a Lagrangian subcategory ⋮ Modular categories with transitive Galois actions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Developments and retrospectives in Lie theory. Geometric and analytic methods. Retrospective selected papers based on the presentations at the seminar ``Lie groups, Lie algebras and their representations, 1991--2014
• Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries
• On gauging symmetry of modular categories
• Anyons in an exactly solved model and beyond
• TFT construction of RCFT correlators. III: Simple currents
• On braided fusion categories. I
• On classification of modular tensor categories
• Module categories, weak Hopf algebras and modular invariants
• Fusion categories of rank 2
• Invariants of spin three-manifolds from Chern-Simons theory and finite-dimensional Hopf algebras
• Fermionic 6j-symbols in superfusion categories
• On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_{2}\) conformal field theories
• Galois extensions of braided tensor categories and braided crossed G-categories
• On the structure of the Witt group of braided fusion categories
• On the gauge equivalence of twisted quantum doubles of elementary Abelian and extra-special 2-groups.
• Level-rank duality via tensor categories
• Nilpotent fusion categories
• A spin decomposition of the verlinde formulas for type A modular categories
• Clifford theory for tensor categories
• Non-Abelian anyons and topological quantum computation
• SIMPLE CURRENTS, MODULAR INVARIANTS AND FIXED POINTS
• Fusion Subcategories of Representation Categories of Twisted Quantum Doubles of Finite Groups
• On the Structure of Modular Categories
• The Level 2 and 3 Modular Invariants for the Orthogonal Algebras
• On braided tensor categories of typeBCD
• The Witt group of non-degenerate braided fusion categories
• Quantum invariants of knots and 3-manifolds
• Quasi Hopf algebras, group cohomology and orbifold models