On the Classification of Bulk and Boundary Conformal Field Theories

Abstract

The classification of rational conformal field theories is reconsidered from the standpoint of boundary conditions. Solving Cardy's equation expressing the consistency condition on a cylinder is equivalent to finding integer valued representations of the fusion algebra. A complete solution not only yields the admissible boundary conditions but also gives valuable information on the bulk properties.

7 pages, LaTeX; minor corrections

References in corpus (3)

• Modular Invariants, Graphs and $\alpha$-Induction for Nets of Subfactors. III
• Applications of braided endomorphisms from conformal inclusions
• Integrable Boundaries, Conformal Boundary Conditions and A-D-E Fusion Rules

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• TFT construction of RCFT correlators IV: Structure constants and correlation functions
• Boundary structure constants for the A-series Virasoro minimal models
• Symmetry breaking boundaries I. General theory
• Boundaries, crosscaps and simple currents
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• The many faces of Ocneanu cells
• Worldsheet approaches to D-branes on supersymmetric cycles
• Conformal Correlation Functions, Frobenius Algebras and Triangulations
• Lectures on Branes in Curved Backgrounds
• Symmetry Breaking Boundary States and Defect Lines
• Quantum brownian motion on a triangular lattice and c=2 boundary conformal field theory
• Klein Bottles and Simple Currents
• Comments on nonunitary conformal field theories
• Non-compact String Backgrounds and Non-rational CFT
• Integrable and Conformal Boundary Conditions for sl(2) A-D-E Lattice Models and Unitary Minimal Conformal Field Theories
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• Non-commutative gauge theory of twisted D-branes
• Exceptional boundary states at c=1
• Integrable Lattice Realizations of Conformal Twisted Boundary Conditions
• Integrable Boundaries, Conformal Boundary Conditions and A-D-E Fusion Rules
• Crossing Kernels for Boundary and Crosscap CFTs
• Defects in the Tri-critical Ising model
• Minimal model boundary flows and c=1 CFT
• D-branes on group manifolds and fusion rings
• Solitonic sectors, alpha-induction and symmetry breaking boundaries
• Crosscaps, Boundaries and T-Duality
• Crosscaps in Gepner Models and Type IIA Orientifolds
• Twenty-five years of two-dimensional rational conformal field theory
• Open Strings in Simple Current Orbifolds
• Crosscap States in Integrable Field Theories and Spin Chains
• Open Descendants of Non-Diagonal Invariants
• Free-field realisation of boundary states and boundary correlation functions of minimal models
• Coulomb-gas approach for boundary conformal field theory
• Coset Graphs in Bulk and Boundary Logarithmic Minimal Models
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• The classifying algebra for defects
• Affine extensions of non-crystallographic Coxeter groups induced by projection
• Properties of RG interfaces for 2D boundary flows
• Orientation matters for NIMreps
• Boundary States and Symplectic Fermions
• Integrable Lattice Realizations of N=1 Superconformal Boundary Conditions
• Finitized Conformal Spectra of the Ising Model on the Klein Bottle and Moebius Strip
• Higher Coxeter graphs associated to affine su(3) modular invariants
• Left-Right Entanglement Entropy, D-Branes, and Level-rank duality
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• Symmetric boundary conditions in boundary critical phenomena
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• Integrable and Conformal Boundary Conditions for Z_k Parafermions on a Cylinder
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