Discussion of D=2 conformal field theory as a functorial field theory, namely as a monoidal functor from a 2d conformal cobordism category to Hilbert spaces:
and including discussion of modular functors:
Graeme Segal, Two-dimensional conformal field theories and modular functors, in: Proceedings of the IXth International Congress on Mathematical Physics, Swansea, 1988, Hilger, Bristol (1989) 22-37.
Graeme Segal, The definition of conformal field theory, in: Ulrike Tillmann (ed.), Topology, geometry and quantum field theory , London Math. Soc. Lect. Note Ser. 308, Cambridge University Press (2004) 421-577 doi:10.1017/CBO9780511526398.019, pdf, pdf
General construction for the case of rational 2d conformal field theory is given by the
See also:
Greg Moore, Graeme Segal, D-branes and K-theory in 2D topological field theory (arXiv:hep-th/0609042)
Richard Blute, Prakash Panangaden, Dorette Pronk, Conformal field theory as a nuclear functor, Electronic Notes in Theoretical Computer Science Volume 172, 1 April 2007, Pages 101-132 GDP Festschrift (pdf, doi:10.1016/j.entcs.2007.02.005)
A different but closely analogous development for chiral 2d CFT (vertex operator algebras, see there for more):
Discussion of the case of Liouville theory:
Early suggestions to refine this to an extended 2-functorial construction:
A step towards generalization to 2d super-conformal field theory:
Discussion of 2-functorial chiral 2d CFT:
Last revised on August 17, 2023 at 22:52:38. See the history of this page for a list of all contributions to it.