A worldsheet extension of O(d,d;Z)

Abstract

We study superconformal interfaces between N=(1,1) supersymmetric sigma models on tori, which preserve a u(1)^{2d} current algebra. Their fusion is non-singular and, using parallel transport on CFT deformation space, it can be reduced to fusion of defect lines in a single torus model. We show that the latter is described by a semi-group extension of O(d,d;Q), and that (on the level of Ramond charges) fusion of interfaces agrees with composition of associated geometric integral transformations. This generalizes the well-known fact that T-duality can be geometrically represented by Fourier-Mukai transformations. Interestingly, we find that the topological interfaces between torus models form the same semi-group upon fusion. We argue that this semi-group of orbifold equivalences can be regarded as the α' deformation of the continuous O(d,d) symmetry of classical supergravity.

71 pages, 1 figure, minor additions and corrections

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• Duality and defects in rational conformal field theory
• Topological defects for the free boson CFT
• Fusion of conformal interfaces
• B-type defects in Landau-Ginzburg models
• D-Branes, RR-Fields and Duality on Noncommutative Manifolds
• Defects and Permutation branes in the Liouville field theory
• The classifying algebra for defects
• Geometry of Topological Defects of Two-dimensional Sigma Models

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• Defects in the Tri-critical Ising model
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• Entanglement entropy at CFT junctions
• More on Non-supersymmetric Asymmetric Orbifolds with Vanishing Cosmological Constant
• On symmetries of N=(4,4) sigma models on T^4
• Entanglement and topological interfaces
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• Hamiltonian truncation in Anti-de Sitter spacetime
• Steady States of Holographic Interfaces
• A note on entanglement entropy for topological interfaces in RCFTs
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• Conformal Janus on Euclidean Sphere
• Boundary RG Flows for Fermions and the Mod 2 Anomaly
• Lie algebra lattices and strings on T-folds
• Fusion of conformal interfaces and bulk induced boundary RG flows
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• Defects, Super-Poincaré line bundle and Fermionic T-duality
• Realizing IR theories by projections in the UV
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• Holographic dual of defect CFT with corner contributions
• Holographic Duality for three-dimensional Super-conformal Field Theories
• Defects and Perturbation
• Interactions of strings on a T-fold
• Non-invertible defects from the Conway SCFT to K3 sigma models I: general results
• Fusion of interfaces in Landau-Ginzburg models: a functorial approach
• Non-invertible symmetries of two-dimensional Non-Linear Sigma Models