Classification of Poisson-Lie T-dual models with two-dimensional targets

Abstract

Four-dimensional Manin triples and Drinfeld doubles are classified and corresponding two-dimensional Poisson-Lie T-dual sigma models on them are constructed. The simplest example of a Drinfeld double allowing decomposition into two nontrivially different Manin triples is presented.

6 pages, LaTeX; correction: two Manin triples originally considered separately are shown to lead to the same Drinfeld double

References in corpus (4)

• Dual Non-Abelian Duality and the Drinfeld Double
• Poisson-Lie T-duality
• Poisson-Lie T-Duality beyond the classical level and the renormalization group
• Poisson-Lie T-Duality and Bianchi Type Algebras

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• Curvature from quantum deformations
• Exact conformal field theories from mutually T-dualizable $\sigma$-models
• Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group $H_4$
• Worldsheet boundary conditions in Poisson-Lie T-duality
• Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models
• Quantization of Drinfel'd doubles
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• The Drinfeld double gl(n) \oplus t_n
• The Poincaré group as a Drinfel'd double
• On the Poisson-Lie T-plurality of boundary conditions
• Poisson-Lie T-plurality revisited. Is T-duality unique?
• Integrability structures in string theory
• Poisson-Lie identities and dualities of Bianchi cosmologies
• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• One-loop renormalizability of all 2d dimensional Poisson-Lie sigma-models
• Non-Abelian T-duality of $Ad{S}_{d\le 3}$ families by Poisson-Lie T-duality
• Classification of standard Manin triples in dimension 4+4
• Classification of six-dimensional Leibniz algebras ${\mathcal E}_3
• Non-Abelian target space duals of Thurston geometries