Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation

Abstract

Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of $SU(2)$ as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum $\mathfrak{su}(2)(\mathbb{R})\dot{\oplus }\mathfrak{a}$, to the fully semisimple Kac-Moody algebra $\mathfrak{sl}(2,\mathbb{C})(\mathbb{R})$. A two-parameter family of models with $SL(2,\mathbb{C})$ as target phase space is obtained so that Poisson-Lie T-duality is realised as an $O(3,3)$ rotation in the phase space. The dual family shares the same phase space but its configuration space is $SB(2,\mathbb{C})$, the Poisson-Lie dual of the group $SU(2)$. A parent action with doubled degrees of freedom on $SL(2,\mathbb{C})$ is defined, together with its Hamiltonian description.

Final amended version. References added. 50 pages

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Cited by in corpus (6)

• Jacobi sigma models
• Principal Chiral Model without and with WZ term: Symmetries and Poisson-Lie T-Duality
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Topological and dynamical aspects of Jacobi sigma models
• The puzzle of global Double Field Theory: open problems and the case for a Higher Kaluza-Klein perspective
• On the classical Integrability of Poisson-Lie T-dual WZW models