A cobordism category of cobordisms equipped with conformal structure.
One way to axiomatize conformal field theory (see there) in FQFT-style is as a suitable monoidal functor on a category of conformal cobordisms (Segal 88).
The definition of conformal field theory , in Differential geometrical methods in theoretical physics (Como, 1987), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 250, Kluwer Acad. Publ., Dordrecht, (1988), 165-171
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.
The definition of conformal field theory , preprint, 1988; also in: Topology, geometry and quantum field theory , ed. U. Tillmann, London Math. Soc. Lect. Note Ser., Vol. 308. Cambridge University Press, Cambridge (2004) 421-577.
Review in the context of the Mumford conjecture:
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 Differential geometrical methods in theoretical physics (Como, 1987), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 250, Kluwer Acad. Publ., Dordrecht, (1988), 165-171
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, preprint, 1988; also in Ulrike Tillmann (ed.) Topology, geometry and quantum field theory , London Math. Soc. Lect. Note Ser., Vol. 308. Cambridge University Press, Cambridge (2004) 421-577. (pdf, pdf)
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)
Tentative suggestions for how to refine this to an extended 2-functorial construction:
A step towards generalization to 2d super-conformal field theory:
Last revised on February 1, 2021 at 11:19:20. See the history of this page for a list of all contributions to it.