Lectures on conformal field theory and Kac-Moody algebras

Abstract

This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.

arXiv comment59 pages, LaTeX2e, extended version of lectures given at the Graduate Course on Conformal Field Theory and Integrable Models (Budapest, August 1996), to appear in Springer Lecture Notes in Physics

References in corpus (33)

• W-symmetry in Conformal Field Theory
• Algebras, BPS States, and Strings
• Completeness Conditions for Boundary Operators in 2D Conformal Field Theory
• Indecomposable Fusion Products
• A matrix S for all simple current extensions
• Conformal Field Theories, Representations and Lattice Constructions
• Irrational Conformal Field Theory
• Simple currents versus orbifolds with discrete torsion -- a complete classification
• The resolution of field identification fixed points in diagonal coset theories
• The Classification of Affine SU(3) Modular Invariant Partition Functions
• Fusion rules in conformal field theory
• Conformal blocks on elliptic curves and the Knizhnik--Zamolodchikov--Bernard equations
• Solutions of the Knizhnik - Zamolodchikov Equation with Rational Isospins and the Reduction to the Minimal Models
• On the Classification of Modular Fusion Algebras
• Galois Modular Invariants of WZW Models
• Fusion, Crossing and Monodromy in Conformal Field Theory Based on $SL(2)$ Current Algebra with Fractional Level
• Nonreductive WZW models and their CFTs
• On $E_{10}$ and the DDF construction
• Global Aspects Of Gauged Wess-Zumino-Witten Models
• Automorphism Modular Invariants of Current Algebras
• An Algebraic Formulation of Level One Wess-Zumino-Witten Models
• W-Algebras, New Rational Models and Completeness of the c = 1 Classification
• Field Identification in Non-Unitary Diagonal Cosets
• Maverick Examples Of Coset Conformal Field Theories
• Superstrings from Hamiltonian Reduction
• Virasoro Singular Vectors via Quantum DS Reduction
• Algebraic Aspects of Orbifold Models
• Construction of Field Algebras with Quantum Symmetry from Local Observables
• An explicit construction of Wakimoto realizations of current algebras
• Quasi-Galois Symmetries of the Modular S-Matrix
• Semi-Classical Blocks and Correlators in Rational and Irrational Conformal Field Theory
• Gauged supersymmetric WZNW model using the BRST approach
• WZNW Models from Non-Standard Bilinear Forms

Cited by in corpus (5)

• Branes: from free fields to general backgrounds
• Noninteraction of waves in two-dimensional conformal field theory
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• On the topological and crosscap entropies in non-oriented RCFTs