Quantization of Wilson loops in Wess-Zumino-Witten models

Abstract

We describe a non-perturbative quantization of classical Wilson loops in the WZW model. The quantized Wilson loop is an operator acting on the Hilbert space of closed strings and commuting either with the full Kac-Moody chiral algebra or with one of its subalgebras. We prove that under open/closed string duality, it is dual to a boundary perturbation of the open string theory. As an application, we show that such operators are useful tools for identifying fixed points of the boundary renormalization group flow.

arXiv comment24 pages. Version published in JHEP

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• A Holographic Model of the Kondo Effect
• Defect loops in gauged Wess-Zumino-Witten models
• On the crossing relation in the presence of defects
• Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
• On the Symmetries of Classical String Theory
• Defect Perturbations in Landau-Ginzburg Models
• Finite higher spin transformations from exponentiation
• The gauging of two-dimensional bosonic sigma models on world-sheets with defects
• Kondo flow invariants, twisted K-theory and Ramond-Ramond charges
• New WZW D-branes from the algebra of Wilson loop operators