On classification of modular tensor categories
From MaRDI portal
Publication:1048148
DOI10.1007/s00220-009-0908-zzbMath1186.18005arXiv0712.1377OpenAlexW2127058163MaRDI QIDQ1048148
Zhenghan Wang, Richard A. Stong, Eric C. Rowell
Publication date: 11 January 2010
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0712.1377
Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).
Related Items (63)
The Witt classes of so(2r)2r ⋮ Generalized ADE classification of topological boundaries and anyon condensation ⋮ Modular categories of dimension $p^3m$ with $m$ square-free ⋮ Tetrahedral symmetry of \(6j\)-symbols in fusion categories ⋮ M-theoretic genesis of topological phases ⋮ Galois conjugation and multiboundary entanglement entropy ⋮ Bantay's trace in unitary modular tensor categories ⋮ Fault-tolerant quantum error correction for non-abelian anyons ⋮ Microscopic description of 2D topological phases, duality, and 3D state sums ⋮ On the classification of the Grothendieck rings of non-self-dual modular categories ⋮ Anyonic entanglement and topological entanglement entropy ⋮ Braided categories of endomorphisms as invariants for local quantum field theories ⋮ Anyonic chains - \(\alpha\)-induction - CFT - defects - subfactors ⋮ Generalisations of Hecke algebras from loop braid groups ⋮ Anyonic chains, topological defects, and conformal field theory ⋮ On classification of fermionic rational conformal field theories ⋮ Unnamed Item ⋮ Reconstructing braided subcategories of \(SU (N)_k \) ⋮ Classification of super-modular categories by rank ⋮ Pseudo-unitary non-self-dual fusion categories of rank 4 ⋮ Rationalizing CFTs and anyonic imprints on Higgs branches ⋮ Hecke relations, cosets and the classification of 2d RCFTs ⋮ Classification of unitary RCFTs with two primaries and central charge less than 25 ⋮ Reconstruction of modular data from \(\mathrm{SL}_2(\mathbb{Z})\) representations ⋮ Meromorphic cosets and the classification of three-character CFT ⋮ On the Grothendieck ring of fusion categories of rank 5 ⋮ Localization of unitary braid group representations ⋮ Fibonacci-type orbifold data in Ising modular categories ⋮ G‐crossed braided zesting ⋮ A finiteness property for braided fusion categories ⋮ Faithful simple objects, orders and gradings of fusion categories ⋮ On classification of extremal non-holomorphic conformal field theories ⋮ Fermionic modular categories and the 16-fold way ⋮ Topological qubit design and leakage ⋮ Modular functors, cohomological field theories, and topological recursion ⋮ Prime decomposition of modular tensor categories of local modules of type D ⋮ Modular categories, integrality and Egyptian fractions ⋮ Lie theory for fusion categories: A research primer ⋮ Dimension as a quantum statistic and the classification of metaplectic categories ⋮ Classification of gapped quantum liquid phases of matter ⋮ Classification of extremal vertex operator algebras with two simple modules ⋮ Non-unitary TQFTs from 3D \(\mathcal{N} = 4\) rank 0 SCFTs ⋮ LOCALIZED ENDOMORPHISMS IN KITAEV'S TORIC CODE ON THE PLANE ⋮ Non-trivially graded self-dual fusion categories of rank 4 ⋮ Congruence subgroups and generalized Frobenius-Schur indicators ⋮ Quantum computation and real multiplication ⋮ A monoidal category for perturbed defects in conformal field theory ⋮ A rigidity result for extensions of braided tensor \(C^*\)-categories derived from compact matrix quantum groups ⋮ Fibonacci topological phase in arrays of anyonic chains ⋮ Slightly trivial extensions of a fusion category ⋮ Fusion structure from exchange symmetry in (2+1)-dimensions ⋮ Rank-finiteness for modular categories ⋮ Mathematics of topological quantum computing ⋮ Non-pseudounitary fusion ⋮ Boundary topological entanglement entropy in two and three dimensions ⋮ On classification of super-modular categories of rank 8 ⋮ Holomorphic modular bootstrap revisited ⋮ Classification of rank 5 premodular categories ⋮ On odd-dimensional modular tensor categories ⋮ 3d TQFTs from Argyres–Douglas theories ⋮ Galois symmetry induced by Hecke relations in rational conformal field theory and associated modular tensor categories ⋮ Modular categories with transitive Galois actions ⋮ Pre-modular fusion categories of small global dimensions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A finiteness property for braided fusion categories
- Quantum groups, quantum categories and quantum field theory
- Anyons in an exactly solved model and beyond
- Classical and quantum conformal field theory
- Topological gauge theories and group cohomology
- Integral modular data and congruences.
- Markov traces and II\(_ 1\) factors in conformal field theory
- State sum invariants of 3-manifolds and quantum \(6j\)-symbols
- Chern-Simons theory with finite gauge group
- A Chern-Simons effective field theory for the Pfaffian quantum Hall state
- Fusion categories of rank 2
- The two-eigenvalue problem and density of Jones representation of braid groups.
- Simulation of topological field theories by quantum computers
- A modular functor which is universal for quantum computation
- Fault-tolerant quantum computation by anyons
- From subfactors to categories and topology. II: The quantum double of tensor categories and subfactors
- Premodular categories, modularisations and invariants of 3-manifolds
- The Frobenius-Schur indicator in conformal field theory
- Modular data: the algebraic combinatorics of conformal field theory
- Density of the \(\text{SO}(3)\) TQFT representation of mapping class groups
- On fusion categories.
- Classification of symmetric polynomials of infinite variables: Construction of Abelian and non-Abelian quantum Hall states
- The search for higher symmetry in string theory
- Non-Abelian anyons and topological quantum computation
- SOME NON-BRAIDED FUSION CATEGORIES OF RANK THREE
- ON EXOTIC MODULAR TENSOR CATEGORIES
- Abelian Chern–Simons theory. I. A topological quantum field theory
- Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134)
- P/NP , and the quantum field computer
- 𝐶* tensor categories from quantum groups
- On the Structure of Modular Categories
- On braided tensor categories of typeBCD
- Topological quantum computation
- Topologization of electron liquids with Chern-Simons theory and quantum computation
- Quantum invariants of knots and 3-manifolds
This page was built for publication: On classification of modular tensor categories