A-D-E Classification of Conformal Field Theories

@article{Cappelli2010ADECO,
  title={A-D-E Classification of Conformal Field Theories},
  author={Andrea Cappelli and Jean-Bernard Zuber},
  journal={Scholarpedia},
  year={2010},
  volume={5},
  pages={10314}
}
The ADE classification scheme is encountered in many areas of mathematics, most notably in the study of Lie algebras. Here such a scheme is shown to describe families of two-dimensional conformal field theories. 

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References

SHOWING 1-10 OF 61 REFERENCES

The ADE Classification of Minimal and A J x ) Conformal Invariant Theories

We present a detailed and complete proof of our earlier conjecture on the classification of minimal conformal invariant theories: This is based on an exhaustive construction of all modular invariant

Modular Invariant Partition Functions in Two-Dimensions

Operator Content of the Ade Lattice Models

The author computes the scaling dimensions of order parameters in ADE lattice models. Some connection is made between the lattice algebra and the operator algebra in conformal invariant theories.

Modular Invariant Partition Functions of Superconformal Theories

Conformal symmetry and multicritical points in two-dimensional quantum field theory

It is shown that exactly solvable ''minimal'' models of two-dimensional conformal quantum field theory describe multicritical points of the scalar field theory with an even polynomial interaction. An

Free field presentation of the An coset models on the torus

The Virasoro algebra

Three theroems are proved. With suitable hypotheses in each case, characterizations are found for the Virasoro algebra, for some of its representations, and for the Ramond-Neveu-Schwarz superalgebra
...