Construction of the Witten-Reshetikhin-Turaev TQFT from conformal field theory

DOI10.1007/s00222-014-0555-7zbMath1328.57030arXiv1110.5027OpenAlexW2963240875MaRDI QIDQ493108

Kenji Ueno, Jørgen Ellegaard Andersen

Publication date: 11 September 2015

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5027

zbMATH Keywords

conformal field theoryquantum groupmoduli spacesmodular functorgeometric quantizationTQFTHitchin connectionskein theorymodular tensor categoryWitten-Reshetikhin-Turaev invariantsFaddeev-Popov ghostsVerlinde bundle

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Topological quantum field theories (aspects of differential topology) (57R56)

Related Items

THE HITCHIN CONNECTION IN ARBITRARY CHARACTERISTIC, Non-semisimple 3-manifold invariants derived from the Kauffman bracket, Conformal nets. II: Conformal blocks, On the Witten–Reshetikhin–Turaev invariants of torus bundles, Asymptotics of the Hilbert-Schmidt norm of curve operators in TQFT, The Witten-Reshetikhin-Turaev invariant for links in finite order mapping tori. I., Notes on Chern–Simons perturbation theory, Non-semisimple TQFT's and BPS \(q\)-series, Resurgence analysis of quantum invariants of Seifert fibered homology spheres, Character varieties as a tensor product, Modular functors, cohomological field theories, and topological recursion, Asymptotic properties of the quantum representations of the mapping class group, A TQFT from quantum Teichmüller theory, The homological content of the Jones representations at q = −1, Asymptotic properties of the Hitchin-Witten connection, Asymptotic expansions of the Witten–Reshetikhin–Turaev invariants of mapping tori I, Boundary conditions for topological quantum field theories, anomalies and projective modular functors, Formal connections for families of star products

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Modular functors are determined by their genus zero data
• The Witten-Reshetikhin-Turaev invariants of finite order mapping tori. II.
• On framings of 3-manifolds
• Fusion rules and modular transformations in 2D conformal field theory
• Classical and quantum conformal field theory
• Conformal field theory with gauge symmetry.
• The Nielsen-Thurston classification of mapping classes is determined by TQFT
• Hecke algebra representations of braid groups and link polynomials
• A q-analogue of Young symmetrizer
• Geometric realization of conformal field theory on Riemann surfaces
• Current algebras and Wess-Zumino model in two dimensions
• Hecke algebras of type \(A_ n\) and subfactors
• Quantum field theory and the Jones polynomial
• Three-manifold invariants derived from the Kauffman bracket
• Involutions on moduli spaces and refinements of the Verlinde formula
• On the TQFT representations of the mapping class groups
• Braids and invariants of 3-manifolds
• Skeins and quantum \(SU(N)\) invariants of 3-manifolds
• Semisimple and modular categories from link invariants
• Skeins, \(SU(N)\) three-manifold invariants and TQFT
• Hecke algebras, modular categories and 3-manifolds quantum invariants
• Ribbon graphs and their invariants derived from quantum groups
• Topological quantum field theories derived from the Kauffman bracket
• On the monodromy of the Hitchin connection
• Invariants of 3-manifolds via link polynomials and quantum groups
• Asymptotics of the Hilbert-Schmidt norm of curve operators in TQFT
• Asymptotic faithfulness of the quantum \(\text{SU}(n)\) representations of the mapping class groups
• Non-additivity of the signature
• Flat connections and geometric quantization
• The Witten–Reshetikhin–Turaev invariants of finite order mapping tori I
• Asymptotics of Toeplitz operators and applications in TQFT
• QUANTUM INVARIANTS OF 3-MANIFOLDS ASSOCIATED WITH CLASSICAL SIMPLE LIE ALGEBRAS
• Hitchin's Projectively Flat Connection, Toeplitz Operators and the Asymptotic Expansion of TQFT Curve Operators
• Topological Quantum Field Theory and the Nielsen–Thurston classification of $M(0,4)$
• AUTOMORPHISM FIXED POINTS IN THE MODULI SPACE OF SEMI-STABLE BUNDLES
• GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY
• CONFORMAL FIELD THEORY AND MODULAR FUNCTOR
• A new polynomial invariant of knots and links
• IDEMPOTENTS OF HECKE ALGEBRAS OF TYPE A
• THREE-MANIFOLD INVARIANTS DERIVED FROM CONFORMAL FIELD THEORY AND PROJECTIVE REPRESENTATIONS OF MODULAR GROUPS
• Sampling the SU(N) Invariants of Three-Manifolds
• CONSTRUCTING TQFTS FROM MODULAR FUNCTORS
• ABELIAN CONFORMAL FIELD THEORY AND DETERMINANT BUNDLES
• Quantum invariants of knots and 3-manifolds
• Hitchin's and WZW connections are the same