# 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.

## 15 Citations

### Defects and perturbation

- Physics
- 2020

We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g -factor, the reflectivity, and…

### Surface operators in 3 d Topological Field Theory and 2 d Rational Conformal Field Theory

- Mathematics
- 2010

We study surface operators in 3d Topological Field Theory and their relations with 2d Rational Conformal Field Theory. We show that a surface operator gives rise to a consistent gluing of chiral and…

### Could McKay Correspondence Generalize in TGD Framework

- Mathematics
- 2017

McKay correspondence states that the McKay graphs for the irreducible representations (irreps) of finite subgroups of G subset SU ( 2 ) characterizing their fusion algebra is given by extended Dynkin…

### Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory

- Mathematics
- 2010

We study surface operators in 3d Topological Field Theory and their relations with 2d Rational Conformal Field Theory. We show that a surface operator gives rise to a consistent gluing of chiral and…

### Universal Bounds on Operator Dimensions in General 2D Conformal Field Theories

- Mathematics
- 2015

We derive a bound on the conformal dimensions of the lightest few states in general unitary 2d conformal field theories with discrete spectra using modular invariance, including CFTs with chiral…

### Spaces of Quantum Field Theories

- Mathematics
- 2010

The concept of a "space of quantum field theories" or "theory space" was set out in the 1970's in work of Wilson, Friedan and others. This structure should play an important role in organizing and…

### Are Higher Structures Needed in the Categorification of TGD

- Physics
- 2017

In this article the idea of n-structure is studied in more detail. A rather radical idea is a formulation of quantum TGD using only cognitive representations consisting of points of space-time…

### Could N = 2 Super-conformal Theories Be Relevant For TGD ?

- Mathematics
- 2019

TGD has as is symmetries super-conformal symmetry (SCS), which is a huge extension of the ordinary SCS. For instance, the infinite-dimensional symplectic group plays the role of finite-dimension…

### Partition functions of non-Abelian quantum Hall states

- Physics
- 2011

Partition functions of edge excitations are obtained for non-Abelian Hall states in the second Landau level, such as the anti-Read–Rezayi state, the Bonderson–Slingerland hierarchy and the Wen…

### Probing thermality beyond the diagonal

- PhysicsPhysical Review D
- 2018

We investigate the off-diagonal sector of eigenstate thermalization using both local and non-local probes in 2-dimensional conformal field theories. A novel analysis of the asymptotics of OPE…

## References

SHOWING 1-10 OF 61 REFERENCES

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

- Mathematics
- 2005

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…

### Operator Content of the Ade Lattice Models

- Mathematics
- 1987

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.

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

- Physics
- 1986

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…

### The Virasoro algebra

- Mathematics
- 1982

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…