Completeness Conditions for Boundary Operators in 2D Conformal Field Theory

Abstract

In non-diagonal conformal models, the boundary fields are not directly related to the bulk spectrum. We illustrate some of their features by completing previous work of Lewellen on sewing constraints for conformal theories in the presence of boundaries. As a result, we include additional open sectors in the descendants of $D_{odd}$ $SU(2)$ WZW models. A new phenomenon emerges, the appearance of multiplicities and fixed-point ambiguities in the boundary algebra not inherited from the closed sector. We conclude by deriving a set of polynomial equations, similar to those satisfied by the fusion-rule coefficients $N_{ij}^k$, for a new tensor $A_{ab}^i$ that determines the open spectrum.

13 pages, Latex, 3 figures

References in corpus (6)

• Dirichlet-Branes and Ramond-Ramond Charges
• Planar Duality in $SU(2)$ WZW Models
• The Open Descendants of Non-Diagonal SU(2) WZW Models
• Sewing Constraints and Non-Orientable Open Strings
• On Structure Constants of $sl(2)$ Theories
• Characterizing Invariants for Local Extensions of Current Algebras

Cited by in corpus (161)

• D-branes and Deformation Quantization
• TFT construction of RCFT correlators I: Partition functions
• Type-I strings on magnetised orbifolds and brane transmutation
• Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
• Boundary Conditions in Rational Conformal Field Theories
• D-branes in Gepner models
• Comments on Open-String Orbifolds with a Non-Vanishing B_{ab}
• Boundary Deformation Theory and Moduli Spaces of D-Branes
• TFT construction of RCFT correlators III: Simple currents
• Instanton Induced Neutrino Majorana Masses in CFT Orientifolds with MSSM-like spectra
• Type I vacua with brane supersymmetry breaking
• TFT construction of RCFT correlators IV: Structure constants and correlation functions
• Surprises in Open-String Perturbation Theory
• Supersymmetry breaking, open strings and M-theory
• Chiral Supersymmetric Standard Model Spectra from Orientifolds of Gepner Models
• Open Strings and D-branes in WZNW model
• Partial breaking of supersymmetry, open strings and M-theory
• Theory and Phenomenology of Type I strings and M-theory
• TFT construction of RCFT correlators II: Unoriented world sheets
• Boundary structure constants for the A-series Virasoro minimal models
• Conformal boundary states for free bosons and fermions
• Symmetry breaking boundaries I. General theory
• Comments on Gepner Models and Type I Vacua in String Theory
• Orientifolds of Gepner Models
• The geometry of WZW branes
• A Note on Toroidal Compactifications of the Type I Superstring and Other Superstring Vacuum Configurations with 16 Supercharges
• On the Classification of Bulk and Boundary Conformal Field Theories
• Permutation Branes
• Boundaries, crosscaps and simple currents
• Symmetry breaking boundaries II. More structures; examples
• Life at the Interface of Particle Physics and String Theory
• The many faces of Ocneanu cells
• Loop Operators and the Kondo Problem
• The conformal boundary states for SU(2) at level 1
• Branes: from free fields to general backgrounds
• Minimal Anomalous U(1)' Extension of the MSSM
• Orientifolds and Mirror Symmetry
• Geometric Couplings and Brane Supersymmetry Breaking
• Charged and Uncharged D-branes in various String Theories
• Non-Supersymmetric Type I Strings with Zero Vacuum Energy
• Conformal Correlation Functions, Frobenius Algebras and Triangulations
• Landau-Ginzburg Realization of Open String TFT
• Projections in string theory and boundary states for Gepner models
• Symmetry Breaking Boundary States and Defect Lines
• A classifying algebra for boundary conditions
• Magnetized Four-Dimensional $Z_2\times Z_2$ Orientifolds
• Bosonization and Scale Invariance on Quantum Wires
• Klein Bottles and Simple Currents
• Comments on nonunitary conformal field theories
• Discrete Gauge Symmetries in Discrete MSSM-like Orientifolds
• Permutation orbifolds
• D-branes in Gepner models and supersymmetry
• Fixed point resolution in extended WZW-models
• Boundary states for WZW models
• Boundary Logarithmic Conformal Field Theory
• Integrable and Conformal Boundary Conditions for sl(2) A-D-E Lattice Models and Unitary Minimal Conformal Field Theories
• Formation of Spherical D2-brane from Multiple D0-branes
• D-branes at Singular Curves of Calabi-Yau Compactifications
• On relevant boundary perturbations of unitary minimal models
• Non-Tachyonic Type 0B Orientifolds, Non-Supersymmetric Gauge Theories and Cosmological RG Flow
• D-branes in String theory Melvin backgrounds
• Type IIB orientifolds on Gepner points
• Chiral Supersymmetric Gepner Model Orientifolds
• Supersymmetric Orientifolds of Gepner Models
• Non-commutative gauge theory of twisted D-branes
• Asymmetric Orientifolds, Brane Supersymmetry Breaking and Non-BPS Branes
• Discrete torsion in non-geometric orbifolds and their open-string descendants
• Completeness of boundary conditions for the critical three-state Potts model
• Open Strings on the Neveu-Schwarz Pentabrane
• Type I Vacua from Diagonal $Z_3$-Orbifolds
• Boundary Conformal Field Theory and Fusion Ring Representations
• Boundary Fixed Points, Enhanced Gauge Symmetry and Singular Bundles on K3
• SU(5) orientifolds, Yukawa couplings, Stringy Instantons and Proton Decay
• Boundary states in coset conformal field theories
• Crossing Kernels for Boundary and Crosscap CFTs
• D-brane charges on non-simply connected groups
• Entanglement branes and factorization in conformal field theory
• Boundary States of c=1 and 3/2 Rational Conformal Field Theories
• Orbifold analysis of broken bulk symmetries
• Crosscaps, Boundaries and T-Duality
• D-branes and BCFT in Hpp-wave backgrounds
• Crosscaps in Gepner Models and Type IIA Orientifolds
• Fermionization and boundary states in 1+1 dimensions
• Twenty-five years of two-dimensional rational conformal field theory
• Open Strings in Simple Current Orbifolds
• Logarithmic conformal field theory with boundary
• On Orientifolds of WZW Models and their Relation to Geometry
• Crosscap States in Integrable Field Theories and Spin Chains
• Boundaries, defects and Frobenius algebras
• D-branes in Singular Calabi-Yau n-fold and N=2 Liouville Theory
• D0-branes in Gepner models and N=2 black holes
• The General Twisted Open WZW String
• Open Descendants of Non-Diagonal Invariants
• A Defect Verlinde Formula
• SU(5) D-brane realizations, Yukawa couplings and proton stability
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
• Canonical quantization of the boundary Wess-Zumino-Witten model
• Free-field realisation of boundary states and boundary correlation functions of minimal models
• Defects and Permutation branes in the Liouville field theory
• Tachyon Condensation on Fuzzy Sphere and Noncommutative Solitons
• Mass scales, supersymmetry breaking and open strings
• (Unoriented) T-folds with few T's
• D-branes in T-fold conformal field theory
• Coulomb-gas approach for boundary conformal field theory
• Novel construction of boundary states in coset conformal field theories
• A new kind of McKay correspondence from non-Abelian gauge theories
• A Note on Partition Functions of Gepner Model Orientifolds
• The classifying algebra for defects
• On gauge couplings and thresholds in Type I Gepner models and otherwise
• Permutation orbifolds of heterotic Gepner models
• Little String Theories in Heterotic Backgrounds
• Free Fermion Orientifolds
• Twisted boundary states and representation of generalized fusion algebra
• Remarks on Global Anomalies in RCFT Orientifolds
• Orientation matters for NIMreps
• Liouville Field Theory on an Unoriented Surface
• Hamiltonian Formulation of Open WZW Strings
• Open Strings and Supersymmetry Breaking
• Open Descendants in Conformal Field Theory
• Orientifolds of SU(2)/U(1) WZW Models
• Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
• Open-string models with broken supersymmetry
• D-branes and orientifolds of SO(3)
• Heterotic-Type II duality and wrapping rules
• Extracting the Luttinger parameter from a single wave function
• On Discrete Symmetries in su(2) and su(3) Affine Theories and Related Graphs
• The three-dimensional origin of the classifying algebra
• Integrable and Conformal Boundary Conditions for Z_k Parafermions on a Cylinder
• Landau-Ginzburg Description of Boundary Critical Phenomena in Two Dimensions
• Lectures on conformal field theory and Kac-Moody algebras
• Bulk from boundary in finite CFT by means of pivotal module categories
• Twisted boundary states in c=1 coset conformal field theories
• Classifying algebras for boundary conditions and traces on spaces of conformal blocks
• Crosscap States for Orientifolds of Euclidean AdS_3
• The WZW model on Random Regge Triangulations
• Superconformal Field Theory with Boundary:Spin Model
• Boundary states in the Nappi-Witten model
• Comments on the classification of orientifolds
• Closed superstring moduli tree-level two-point scattering amplitudes in Type IIB orientifold on $T^6/(Z_2\times Z_2)$
• Permutation Orientifolds of Gepner Models
• Magnetic Fluxes, NS-NS $B$ Field and Shifts in Four-Dimensional Orientifolds
• Permutation Orientifolds
• Formula for Fixed Point Resolution Matrix of Permutation Orbifolds
• Coulomb-gas formulation of SU(2) branes and chiral blocks
• A Lightning Introduction to String Theory
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• On the topological and crosscap entropies in non-oriented RCFTs
• Crosscap states and duality of Ising field theory in two dimensions
• Recent Trends in Superstring Phenomenology
• D-brane conformal field theory
• Issues on tadpoles and vacuum redefinitions in String Theory
• Permutation Orbifolds in Conformal Field Theories and String Theory
• On Orientifolds of c=1 Orbifolds
• Bootstrapping Boundaries and Branes
• Open strings in Lie groups and associative products
• On Cardy states in the (2,2,2,2) Gepner model
• Non periodic Ishibashi states: the su(2) and su(3) affine theories
• Bundles of chiral blocks and boundary conditions in CFT
• Anomalous U(1), Dark Matter and Asymmetry
• The scientific work of Sonia Stanciu
• Superstrings beyond one loop