Irrational Conformal Field Theory

Abstract

This is a review of irrational conformal field theory, which includes rational conformal field theory as a small subspace. Central topics of the review include the Virasoro master equation, its solutions and the dynamics of irrational conformal field theory. Discussion of the dynamics includes the generalized Knizhnik-Zamolodchikov equations on the sphere, the corresponding heat-like systems on the torus and the generic world- sheet action of irrational conformal field theory.

195 pages, Latex, 12 figures, to appear in Physics Reports. Typos corrected in Sections 13 and 14, and a footnote added in Section 14

References in corpus (29)

• W-symmetry in Conformal Field Theory
• A WZW model based on a non-semi-simple group
• String Propagation in Gravitational Wave Backgrounds
• Nonsemisimple Sugawara Constructions
• A Class of String Backgrounds as a Semiclassical Limit of WZW Models
• Superstring Gravitational Wave Backgrounds with Spacetime Supersymmetry
• Gauging a Non-Semi-Simple WZW Model
• On Bosonic and Supersymmetric Current Algebras for Non-Semi-Simple Groups
• Exact string background from a WZW model based on the Heisenberg group
• On a `universal' class of WZW-type conformal models
• The BRST formulation of G/H WZNW models
• Exact string backgrounds from WZW models based on non-semi-simple groups
• Plane Gravitational Waves in String Theory
• The Lie h-Invariant Conformal Field Theories and the Lie h-Invariant Graphs
• Manin triples and $N=2$ superconformal field theory
• General branching functions of affine Lie algebras
• Linearized Form of the Generic Affine-Virasoro Action
• Ward Identities for Affine-Virasoro Correlators
• The Conformal Points Of The Generalized Thirring Model
• Affine Algebras, $N=2$ Superconformal Algebras, and Gauged WZNW Models
• N=2 Current Algebras for Non-Semi-Simple Groups
• W3 Constructions on Affine Lie Algebras
• Flat Connections for Characters in Irrational Conformal Field Theory
• Conformal Blocks of Coset Construction: Zero Ghost Number
• Solving the Ward Identities of Irrational Conformal Field Theory
• Flat Connections and Non-Local Conserved Quantities in Irrational Conformal Field Theory
• Generalised Virasoro Constructions from Affine Inonu-Wigner Contractions
• Some Comments on Lie-Poisson Structure of Conformal Non-Abelian Thirring Models
• Conformal Invariance of Interacting WZNW Models

Cited by in corpus (52)

• String Theory and the Path to Unification: A Review of Recent Developments
• Superbranes and Superembeddings
• Entanglement Scrambling in 2d Conformal Field Theory
• One-Dimensional Quasi-Exactly Solvable Schrödinger Equations
• Systematic approach to cyclic orbifolds
• Product CFTs, gravitational cloning, massive gravitons and the space of gravitational duals
• Exotic RG Flows from Holography
• Knizhnik-Zamolodchikov equations and spectral flow in AdS3 string theory
• Origin of Logarithmic Operators in Conformal Field Theories
• On the Beta Function for Anisotropic Current Interactions in 2D
• M-theory and E10: Billiards, Branes, and Imaginary Roots
• Coupled minimal models revisited
• Conformal Sigma Models for a Class of $T^{p,q}$ Spaces
• Twenty-five years of two-dimensional rational conformal field theory
• Large-N limits of 2d CFTs, Quivers and AdS_3 duals
• Two Large Examples in Orbifold Theory: Abelian Orbifolds and the Charge Conjugation Orbifold on su(n)
• Knizhnik-Zamolodchikov-type equations for gauged WZNW models
• Integrable Generalized Principal Chiral Models
• The General Twisted Open WZW String
• On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation
• The General Coset Orbifold Action
• A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states
• The Outer-Automorphic WZW Orbifolds on so(2n), including Five Triality Orbifolds on so(8)
• Cyclic Coset Orbifolds
• On the Target-Space Geometry of Open-String Orientation-Orbifold Sectors
• Extended Operator Algebra and Reducibility in the WZW Permutation Orbifolds
• Coset Construction of Noncompact Spin(7) and G_2 CFTs
• Strong Coupling Fixed Points of Current Interactions and Disordered Fermions in 2D
• Twisted Einstein Tensors and Orbifold Geometry
• Hamiltonian Formulation of Open WZW Strings
• New Semiclassical Nonabelian Vertex Operators for Chiral and Nonchiral WZW Theory
• Twisted Open Strings from Closed Strings: The WZW Orientation Orbifolds
• Sugawara form for AdS superstring
• A Basic Class of Twisted Open WZW Strings
• Integrable Generalized Thirring Model
• Renormalization group for network models of Quantum Hall transitions
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Lectures on conformal field theory and Kac-Moody algebras
• Deformations of WZW models
• New Spin-Two Gauged Sigma Models and General Conformal Field Theory
• Hamiltonian Reduction of Supersymmetric WZNW Models on Bosonic Groups and Superstrings
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26. I.Extended Actions and New Twisted World-Sheet Gravities
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 II. The Twisted BRST Systems of \hatc=52 Matter
• On the Large N Limit of Conformal Field Theory
• The Orbifolds of Permutation-Type as Physical String Systems at Multiples of $\mathbf{c}=26$ V. Cyclic Permutation Orbifolds
• 2D induced gravity from canonically gauged WZNW system
• Two-Dimensional Supersymmetric Sigma Models on Almost-Product Manifolds and Non-Geometry
• Asymmetric Galilean conformal algebras
• Sugawara Construction for Higher Genus Riemann Surfaces
• Hidden symmetries in two dimensional field theory
• Operator quantization of constrained WZNW theories and coset constructions
• Conformal Models of Thirring Type and the Affine Virasoro Construction