Novel construction of boundary states in coset conformal field theories
arXiv:hep-th/0207177 · doi:10.1016/S0550-3213(02)01011-8
Abstract
We develop a systematic method to solve the Cardy condition for the coset conformal field theory G/H. The problem is equivalent to finding a non-negative integer valued matrix representation (NIM-rep) of the fusion algebra. Based on the relation of the G/H theory with the tensor product theory G x H, we give a map from NIM-reps of G x H to those of G/H. Our map provides a large class of NIM-reps in coset theories. In particular, we give some examples of NIM-reps not factorizable into the G and the H sectors. The action of the simple currents on NIM-reps plays an essential role in our construction. As an illustration of our procedure, we consider the diagonal coset SU(2)_5 x SU(2)_3 /SU(2)_8 to obtain a new NIM-rep based on the conformal embedding su(2)_3 \oplus su(2)_8 \subset sp(6)_1.
arXiv comment43 pages, 6 figures; (v2) arguments about the actions of simple currents on NIM-reps modified. references added; (v3) misplaced figure corrected
References in corpus (34)
- Completeness Conditions for Boundary Operators in 2D Conformal Field Theory
- Boundary Conditions in Rational Conformal Field Theories
- Modular Invariants, Graphs and -Induction for Nets of Subfactors. III
- Applications of braided endomorphisms from conformal inclusions
- Geometrical interpretation of D-branes in gauged WZW models
- Chiral structure of modular invariants for subfactors
- Boundary structure constants for the A-series Virasoro minimal models
- Symmetry breaking boundaries I. General theory
- Conformal boundary states for free bosons and fermions
- Boundaries, crosscaps and simple currents
- Symmetry breaking boundaries II. More structures; examples
- Modular Invariants, Graphs and -Induction for Nets of Subfactors I
- The conformal boundary states for SU(2) at level 1
- Conformal boundary conditions and three-dimensional topological field theory
- The resolution of field identification fixed points in diagonal coset theories
- Symmetry Breaking Boundary States and Defect Lines
- Modular Invariants, Graphs and -Induction for Nets of Subfactors II
- Boundary states for WZW models
- D-Branes in Coset Models
- Structure constants for the D-series Virasoro minimal models
- D-Branes on a gauged WZW model
- Exceptional boundary states at c=1
- Boundary Conformal Field Theory and Fusion Ring Representations
- Boundary states in coset conformal field theories
- Solitonic sectors, alpha-induction and symmetry breaking boundaries
- On boundary RG-flows in coset conformal field theories
- On Superpotentials for D-Branes in Gepner Models
- On the Classification of Diagonal Coset Modular Invariants
- D-branes in asymmetrically gauged WZW models and axial-vector duality
- Maverick Examples Of Coset Conformal Field Theories
- Characters for Coset Conformal Field Theories
- Maximally symmetric D-branes in gauged WZW models
- A Note on c=1 Virasoro Boundary States and Asymmetric Shift Orbifolds
- Comments on D-branes in Kazama-Suzuki models and Landau-Ginzburg theories
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- Level-rank duality of untwisted and twisted D-branes
- Twisted boundary states in Kazama-Suzuki models
- D-branes and matrix factorisations in supersymmetric coset models
- 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
- Algebraic properties of CFT coset construction and Schramm-Loewner evolution
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- Fusion of interfaces in Landau-Ginzburg models: a functorial approach
- Bootstrapping Boundaries and Branes