On the structure of unitary conformal field theory. I: Existence of conformal blocks

DOI10.1007/BF01219658zbMath0683.46053OpenAlexW2079984460MaRDI QIDQ1824835

Yanyan Li

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1007/bf01219658

zbMATH Keywords

chiral algebraschiral fieldsEuclidean Green functions of the scaling fieldsmathematical structure of unitary rational conformal field theories in two dimensionsmatrix elements of Yang-Baxter- or braid-matrices

Mathematics Subject Classification ID

Constructive quantum field theory (81T08) Lie algebras and Lie superalgebras (17B99) Miscellaneous applications of functional analysis (46N99)

Related Items

Matrix product approximations to conformal field theories ⋮ Classical limit of irregular blocks and Mathieu functions ⋮ Fock representations of quantum fields with generalized statistics ⋮ MARKOV QUANTUM FIELDS ON A MANIFOLD ⋮ Wightman fields for two-dimensional conformal field theories with pointed representation category ⋮ Braid matrices and structure constants for minimal conformal models ⋮ Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks ⋮ On the structure of unitary conformal field theory. II: Representation theoretic approach ⋮ Transition amplitudes and sewing properties for bosons on the Riemann sphere ⋮ Space-time fields and exchange fields ⋮ Braiding properties of the \(N = 1\) super-conformal blocks (Ramond sector) ⋮ Branes: From free fields to general backgrounds ⋮ On structure constants of \(\text{sl}(2)\) theories. ⋮ More transition amplitudes on the Riemann sphere ⋮ Duality and modular invariance in rational conformal field theories

Cites Work

• On virtual representations of symmetric spaces and their analytic continuation
• Classical and quantum conformal field theory
• Unitary representations of the Virasoro and super-Virasoro algebras
• Projective unitary positive-energy representations of \(Diff(S^ 1)\)
• Infinite conformal symmetry in two-dimensional quantum field theory
• Current algebras and Wess-Zumino model in two dimensions
• Locality of conformal fields in two dimensions: Exchange algebra on the light-cone
• Euclidean formulation of quantum field theory without positivity
• Axioms for Euclidean Green's functions
• Stable cohomology of the algebra \(W_ n\) and relations of the algebra \(L_ 1\)
• Mapping class groups and their relationship to braid groups
• The current algebra on the circle as a germ of local field theories