http://cds.cern.ch/record/241379/files/arXiv:hep-th_9210010.pdf

W symmetry in conformal field theory

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 sesquilinear forms, with positive integral coefficients, in the characters of the Virasoro or of theA1(1) Kac-Moody algebras, which describe the corresponding partition functions on a torus. A remarkable correspondence emerges with simply laced Lie algebras.

/pdf/the-a-d-e-classification-of-minimal-anda-1-1-conformal-2l3b2dpywo.pdf

The A-D-E classification of minimal andA 1 (1) conformal invariant theories

These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. 
Contents: 
1. Conformal theories in d dimensions 
2. Conformal theories in 2 dimensions 
3. The central charge and the Virasoro algebra 
4. Kac determinant and unitarity 
5. Identication of m = 3 with the critical Ising model 
6. Free bosons and fermions 
7. Free fermions on a torus 
8. Free bosons on a torus 
9. Affine Kac-Moody algebras and coset constructions 
10. Advanced applications

Applied Conformal Field Theory

Non-Abelian anyons—particles whose exchange noncommutatively transforms a system’s quantum state—are widely sought for the exotic fundamental physics they harbour and for quantum computing applications. Numerous blueprints now exist for stabilizing the simplest type of non-Abelian anyon, defects binding Majorana modes, by interfacing widely available materials. Here we introduce a device fabricated from conventional fractional quantum Hall states and s-wave superconductors that supports exotic non-Abelian defects binding parafermionic zero modes, which generalize Majorana bound states. We show that these new modes can be experimentally identified (and distinguished from Majoranas) using Josephson measurements. We also provide a practical recipe for braiding parafermionic zero modes and show that they give rise to non-Abelian statistics. Interestingly, braiding in our setup produces a richer set of topologically protected operations when compared with the Majorana case. As a byproduct, we establish a new, experimentally realistic Majorana platform in weakly spin–orbit-coupled materials such as gallium arsenide.

/pdf/exotic-non-abelian-anyons-from-conventional-fractional-1bks1ss5io.pdf

Exotic non-Abelian anyons from conventional fractional quantum Hall states

/pdf/vertex-operators-in-conformal-field-theory-on-mathbb-p-1-and-4xvanxbse4.pdf

Vertex Operators in Conformal Field Theory on $\mathbb{P}^{1}$ and Monodromy Representations of Braid Group

A two-dimensional exactly solvable model of a conformal quantum field theory is developed which is self-dual and has Z/sub N/ symmetry. The operator algebra, the correlation functions, and the anomalous dimensions of all fields are calculated for this model, which describes self-dual critical points in Z/sub N/-symmetric statistical systems.

Nonlocal (parafermion) currents in two-dimensional conformal quantum field theory and self-dual critical points in Z/sub N/-symmetric statistical systems

V.A. Fateev

Papers

Nonlocal (parafermion) currents in two-dimensional conformal quantum field theory and self-dual critical points in Z/sub N/-symmetric statistical systems