nLab D=2 CFT as functorial field theory -- references

CFT as functorial field theory

D=2D=2 CFT as functorial field theory

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:

  • Graeme Segal, The definition of conformal field theory, in: K. Bleuler, M. Werner (eds.), Differential geometrical methods in theoretical physics (Proceedings of Research Workshop, Como 1987), NATO Adv. Sci. Inst., Ser. C: Math. Phys. Sci. 250 Kluwer Acad. Publ., Dordrecht (1988) 165-171 [[doi:10.1007/978-94-015-7809-7]]

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]]

See also:

A different but closely analogous development for chiral 2d CFT (vertex operator algebras, see there for more):

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 June 9, 2022 at 07:16:37. See the history of this page for a list of all contributions to it.