algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
functorial quantum field theory
Reshetikhin?Turaev model? / Chern-Simons theory
FQFT and cohomology
Rational 2d conformal field theories are that class of relatively simple 2d CFTs, such as the WZW model, which are characterized by the fact that their spaces of conformal blocks are finite dimensional vector spaces. Locally such 2d CFTs are given by a rational vertex operator algebra.
Interpreted as perturbative string theory vacua, rational 2d CFTs correspond to (non-geometric) target spaces which are compact (such as fibers of Kaluza-Klein compactifications, but not Minkowski spacetime, for instance). See e.g. Schomerus 05 for contrast.
The FRS-theorem on rational 2d CFT provides a complete classification of rational 2d CFT via the CS-WZW correspondence and the Reshetikhin-Turaev construction of 3d Chern-Simons theory.
See the references at FRS-theorem on rational 2d CFT.
Lecture notes on modular tensor categories and rational CFT:
The contrast with non-rational CFTs:
See also:
Classification:
Constructing correlators in rational conformal field theory via string net models:
Last revised on January 10, 2023 at 05:57:28. See the history of this page for a list of all contributions to it.