nLab rational 2d conformal field theory

Contents

Context

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Functorial Quantum field theory

Contents

Idea

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.

Properties

Classification

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.

Examples

References

See the references at FRS-theorem on rational 2d CFT.

Lecture notes on modular tensor categories and rational CFT:

  • Ingo Runkel, Algebra in Braided Tensor Categories and Conformal Field Theory (pdf, pdf)

The contrast with non-rational CFTs:

See also:

  • Zhihao Duan, Kimyeong Lee, Kaiwen Sun, Hecke Relations, Cosets and the Classification of 2d RCFTs [[arXiv:2206.07478]]

Classification:

  • Sunil Mukhi, Brandon C. Rayhaun, Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25 [arXiv:2208.05486]

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.