TFT construction of RCFT correlators III: Simple currents

Abstract

We use simple currents to construct symmetric special Frobenius algebras in modular tensor categories. We classify such simple current type algebras with the help of abelian group cohomology. We show that they lead to the modular invariant torus partition functions that have been studied by Kreuzer and Schellekens. We also classify boundary conditions in the associated conformal field theories and show that the boundary states are given by the formula proposed in hep-th/0007174. Finally, we investigate conformal defects in these theories.

78 pages, table of contents, several figures; v2: corrected definition 2.20, added remark to section 4.3

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• Topological Defects on the Lattice I: The Ising model
• Correspondences of ribbon categories
• Defect lines, dualities, and generalised orbifolds
• Topological defects for the free boson CFT
• TFT construction of RCFT correlators IV: Structure constants and correlation functions
• Chiral Supersymmetric Standard Model Spectra from Orientifolds of Gepner Models
• Construction of two-dimensional topological field theories with non-invertible symmetries
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• Anomalies and Bounds on Charged Operators
• Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras
• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• Schur-Weyl Duality for Heisenberg Cosets
• Cardy algebras and sewing constraints, I
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
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• Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond
• Generalized string-nets for unitary fusion categories without tetrahedral symmetry
• Simple current extensions beyond semi-simplicity
• Fusion rules and boundary conditions in the c=0 triplet model
• Higher categorical symmetries and gauging in two-dimensional spin systems
• Numerical evidence for a Haagerup conformal field theory
• Non-compact String Backgrounds and Non-rational CFT
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• Morita classes of algebras in modular tensor categories
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• Orbifolds of n-dimensional defect TQFTs
• Invertible defects and isomorphisms of rational CFTs
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• A modular invariant bulk theory for the c=0 triplet model
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• The Moonshine Anomaly
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• Parity and Spin CFT with boundaries and defects
• Building vertex algebras from parts
• Logarithmic bulk and boundary conformal field theory and the full centre construction
• Non-local conserved charges from defects in perturbed conformal field theory
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• Logarithmic conformal field theories of type $B_n,\ell =4$ and symplectic fermions
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• Domain walls between 3d phases of Reshetikhin-Turaev TQFTs
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• Extend The Levin-Wen Model To Two-dimensional Topological Orders With Gapped Boundary Junctions
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• Klein Topological Field Theories from Group Representations
• TFT construction of RCFT correlators V: Proof of modular invariance and factorisation
• On the geometry of coset branes
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• CFT Correlators for Cardy Bulk Fields via String-Net Models
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