Loop Operators and the Kondo Problem

Abstract

We analyse the renormalisation group flow for D-branes in WZW models from the point of view of the boundary states. To this end we consider loop operators that perturb the boundary states away from their ultraviolet fixed points, and show how to regularise and renormalise them consistently with the global symmetries of the problem. We pay particular attention to the chiral operators that only depend on left-moving currents, and which are attractors of the renormalisation group flow. We check (to lowest non-trivial order in the coupling constant) that at their stable infrared fixed points these operators measure quantum monodromies, in agreement with previous semiclassical studies. Our results help clarify the general relationship between boundary transfer matrices and defect lines, which parallels the relation between (non-commutative) fields on (a stack of) D-branes and their push-forwards to the target-space bulk.

22 pages, 2 figures

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• Construction of two-dimensional topological field theories with non-invertible symmetries
• Fusion of conformal interfaces
• Unifying Constructions of Non-Invertible Symmetries
• Defects and Bulk Perturbations of Boundary Landau-Ginzburg Orbifolds
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• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• A worldsheet extension of O(d,d;Z)
• A Holographic Model of the Kondo Effect
• B-type defects in Landau-Ginzburg models
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• Defect flows in minimal models
• Bulk flows in Virasoro minimal models with boundaries
• Comments on Non-invertible Symmetries in Argyres-Douglas Theories
• Non-supersymmetric Asymmetric Orbifolds with Vanishing Cosmological Constant
• Perturbed Defects and T-Systems in Conformal Field Theory
• Dirichlet sigma models and mean curvature flow
• Defect loops in gauged Wess-Zumino-Witten models
• 't Hooft Operators in Gauge Theory from Toda CFT
• Integrable Kondo problems
• On the crossing relation in the presence of defects
• Entanglement and topological interfaces
• Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
• Entanglement evolution across a conformal interface
• Factorization Conjecture and the Open/Closed String Correspondence
• First-principles derivation of the AdS/CFT Y-systems
• Quantization of Wilson loops in Wess-Zumino-Witten models
• Calabi's diastasis as interface entropy
• On the Symmetries of Classical String Theory
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• ABCD of Kondo effect
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• Type-II defects in the super-Liouville theory
• On supersymmetric interfaces for string theory
• Defects, Super-Poincaré line bundle and Fermionic T-duality
• Fusion of conformal interfaces and bulk induced boundary RG flows
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• The Hirota equation for string theory in AdS5xS5 from the fusion of line operators
• A Monoidal Category for Perturbed Defects in Conformal Field Theory
• Kondo flow invariants, twisted K-theory and Ramond-Ramond charges
• Boundary Criticality of Complex Conformal Field Theory: A Case Study in the Non-Hermitian 5-State Potts Model
• Brane Bulk Couplings and Condensation from REA Fusion
• Anisotropic Kondo line defect and ODE/IM correspondence
• Fusion of interfaces in Landau-Ginzburg models: a functorial approach
• Twisted WZW Branes from Twisted REA's
• New WZW D-branes from the algebra of Wilson loop operators
• Quasi-Hamiltonian bookkeeping of WZNW defects
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