ABELIAN CONFORMAL FIELD THEORY AND DETERMINANT BUNDLES

DOI10.1142/S0129167X07004369zbMath1128.81026arXivmath/0304135MaRDI QIDQ5296113

Kenji Ueno, Jørgen Ellegaard Andersen

Publication date: 1 August 2007

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0304135

zbMATH Keywords

conformal field theorytopological quantum field theorydeterminant line bundlesmodular functors

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Topological field theories in quantum mechanics (81T45) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Topological quantum field theories (aspects of differential topology) (57R56)

Related Items

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., Berezin-Toeplitz quantization for compact Kähler manifolds. A review of results, Convergence of sewing conformal blocks, Resurgence analysis of quantum invariants of Seifert fibered homology spheres, Enumeration of chord diagrams on many intervals and their non-orientable analogs, Character varieties as a tensor product, Modular functors are determined by their genus zero data, Hitchin's connection, Toeplitz operators, and symmetry invariant deformation quantization, Hitchin's connection in metaplectic quantization, The Witten-Reshetikhin-Turaev invariants of finite order mapping tori. II., Modular functors, cohomological field theories, and topological recursion, Construction of the Witten-Reshetikhin-Turaev TQFT from conformal field theory, On the unitary nature of abelian conformal blocks, On the holomorphic point of view in the theory of quantum knot invariants, 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, Formal connections for families of star products

Cites Work

• Geometric realization of conformal field theory on Riemann surfaces
• Theta functions on Riemann surfaces
• Asymptotic faithfulness of the quantum \(\text{SU}(n)\) representations of the mapping class groups
• GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY