Poisson-Lie T-duality and loop groups of Drinfeld doubles

1995/12/06 by C. Klimčı́k, C. Klimcik, Pavol Ševera +1 · 16 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.1016/0370-2693(96)00025-1

published as Phys.Lett. B372 (1996) 65-71 · 15 pages, LaTeX

arxiv created 1995/12/06 · openalex publication_date 1996/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A duality invariant first order action is constructed on the loop group of a Drinfeld double. It gives at the same time the description of both of the pair of σ-models related by Poisson-Lie T-duality. Remarkably, the action contains a WZW-term on the Drinfeld double not only for conformally invariant \si-models. The resulting actions of the models from the dual pair differ just by a total derivative corresponding to an ambiguity in specifying a two-form whose exterior derivative is the WZW three-form. This total derivative is nothing but the Semenov-Tian-Shansky symplectic form on the Drinfeld double and it gives directly a generating function of the canonical transformation relating the \si-models from the dual pair.

Citations

• Poisson-Lie T-duality: the path-integral derivation
• T-duality in arbitrary string backgrounds

Cited by

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• Twists of trigonometric sigma models
• Comments on Dualities on Group Manifolds and Supersymmetry
• Dressing cosets revisited
• Recent developments in non‐Abelian T‐duality in string theory
• Cosmological string backgrounds from super Poisson-Lie T-plurality
• T-dualization of Gödel string cosmologies via Poisson–Lie T-duality approach
• One-loop renormalizability of all 2-dimensional Poisson–Lie σ-models
• Yang–Baxter σ model: Quantum aspects
• Poisson-Lie T-duality: Open strings and D-branes
• Current algebras, generalised fluxes and non-geometry
• Poisson–Lie T-duality beyond the classical level and the renormalization group