Abstract
The doubled target space of the fundamental closed string is identified with its phase space and described by an almost para-Hermitian geometry. We explore this setup in the context of group manifolds which admit a maximally isotropic subgroup. This leads to a formulation of the Poisson-Lie σ-model and Poisson-Lie T-duality in terms of para-Hermitian geometry. The emphasis is put on so called half-integrable setups where only one of the Lagrangian subspaces of the doubled space has to be integrable. Using the dressing coset construction in Poisson-Lie T-duality, we extend our construction to more general coset spaces. This allows to explicitly obtain a huge class of para-Hermitian geometries. Each of them is automatically equipped which a generalized frame field, required for consistent generalized Scherk-Schwarz reductions. As examples we present integrable λ- and η-deformations on the three- and two-sphere.
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Hassler, F., Lüst, D. & Rudolph, F.J. Para-Hermitian geometries for Poisson-Lie symmetric σ-models. J. High Energ. Phys. 2019, 160 (2019). https://doi.org/10.1007/JHEP10(2019)160
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DOI: https://doi.org/10.1007/JHEP10(2019)160