Abstract
We generalize the Poisson–Lie T-duality by making use of the structure of the affine Poisson group which is the concept introduced some time ago in Poisson geometry as a generalization of the Poisson–Lie group. We also introduce a new notion of an affine quasi-Poisson group and show that it gives rise to a still more general T-duality framework. We establish for a class of examples that this new T-duality is compatible with the renormalization group flow.
Highlights
The Poisson-Lie T-duality [1] is the framework which permits to construct examples of dynamically equivalent non-linear σ-models living on geometrically non-equivalent backgrounds
The basic structural ingredient underlying this kind of T-duality is the so called Drinfeld double D, which is a Lie group equipped with a bi-invariant metric of maximally Lorentzian signature and having two halfdimensional isotropic subgroups K and K
We stress that the concept of the affine quasi-Poisson group is a new one and we introduce it in the present paper
Summary
The Poisson-Lie T-duality [1] is the framework which permits to construct examples of dynamically equivalent non-linear σ-models living on geometrically non-equivalent backgrounds. The existence of the non-trivial symplectomorphisms LDL → LDR pulling back the Hamiltonian QER onto the Hamiltonian QEL is by no means an obvious thing, we shall show in the present paper that such symplectomorphisms do exist for many choices of the Drinfeld doubles DL, DR This fact leads to a substantial enlargement of the non-Abelian T-duality group as defined in [7] since the vertical arrow symplectomorphisms in the scheme (2.16) makes possible to ”travel” between the Poisson-Lie T-dualities based on the different subspaces EL ⊂ DL and ER ⊂ DR. The right vertical symplectomorphisms exists and establishes the affine (quasi-)Poisson T-duality relating the σ-models (1.6) and (1.7)
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