Invertible defects and isomorphisms of rational CFTs

Abstract

Given two two-dimensional conformal field theories, a domain wall -- or defect line -- between them is called invertible if there is another defect with which it fuses to the identity defect. A defect is called topological if it is transparent to the stress tensor. A conformal isomorphism between the two CFTs is a linear isomorphism between their state spaces which preserves the stress tensor and is compatible with the operator product expansion. We show that for rational CFTs there is a one-to-one correspondence between invertible topological defects and conformal isomorphisms if both preserve the rational symmetry. This correspondence is compatible with composition.

20 pages, 17 figures.

References in corpus (31)

• The Large N Limit of Superconformal Field Theories and Supergravity
• String-net condensation: A physical mechanism for topological phases
• Target Space Duality in String Theory
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Duality and defects in rational conformal field theory
• Generalised twisted partition functions
• Boundary conformal field theory approach to the two-dimensional critical Ising model with a defect line
• Permeable conformal walls and holography
• Kramers-Wannier duality from conformal defects
• TFT construction of RCFT correlators III: Simple currents
• An algebraic approach to logarithmic conformal field theory
• Correspondences of ribbon categories
• Topological defects for the free boson CFT
• Reflection and Transmission for Conformal Defects
• TFT construction of RCFT correlators IV: Structure constants and correlation functions
• Fusion of conformal interfaces
• Conformal boundary conditions and three-dimensional topological field theory
• Cardy algebras and sewing constraints, I
• Conformal Correlation Functions, Frobenius Algebras and Triangulations
• Vertex Algebras, Mirror Symmetry, And D-Branes: The Case Of Complex Tori
• Full field algebras
• Bi-branes: Target Space Geometry for World Sheet topological Defects
• Morita classes of algebras in modular tensor categories
• Axiomatic Conformal Field Theory
• Categorification and correlation functions in conformal field theory
• Abelian duality, walls and boundary conditions in diverse dimensions
• The fusion algebra of bimodule categories
• Cardy condition for open-closed field algebras
• Discrete symmetries of unitary minimal conformal theories
• Full field algebras, operads and tensor categories
• Gerbe-holonomy for surfaces with defect networks

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• Generalized Global Symmetries
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• Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
• Construction of two-dimensional topological field theories with non-invertible symmetries
• Anomalies and Bounds on Charged Operators
• Symmetry as a shadow of topological order and a derivation of topological holographic principle
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• A worldsheet extension of O(d,d;Z)
• Decorated ${\mathbb{Z}}_2$ Symmetry Defects and Their Time-Reversal Anomalies
• Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers
• Lorentzian Dynamics and Factorization Beyond Rationality
• Non-Equilibrium Conformal Field Theories with Impurities
• The center functor is fully faithful
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• Quantum Statistics and Spacetime Topology: Quantum Surgery Formulas
• Pointed Drinfeld center functor
• The classifying algebra for defects
• RCFT with defects: Factorization and fundamental world sheets
• Two-dimensional Anomaly, Orbifolding, and Boundary States
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Geometry of Topological Defects of Two-dimensional Sigma Models
• Defects in G/H coset, G/G topological field theory and discrete Fourier-Mukai transform
• Poisson-Lie T-duality defects and target space fusion
• The Symmetry Enriched Center Functor is Fully Faithful
• Bootstrapping Boundaries and Branes
• Fibonacci topological phase in arrays of anyonic chains