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.
Highlights
A dual σ-model after applying a procedure due to Buscher [3, 4]
The doubled target space of the fundamental closed string is identified with its phase space and described by an almost para-Hermitian geometry
And even after quantization, the dynamics of both models is indistinguishable. This is remarkable because the dual target space looks in general quite different compared to the original one
Summary
We present the mathematical background which we apply to the Poisson-Lie σ-model. This forms the basis to define Born geometry and has been established in [47,48,49], for an executive summary see [65]
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