Para-Hermitian geometries for Poisson-Lie symmetric -models
May 9, 2019
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Abstract: (Springer)
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.Note:
- 30 pages, v2: references add, minor typos corrected
- Differential and Algebraic Geometry
- Sigma Models
- String Duality
- Flux compactifications
- string: closed
- geometry
- integrability
- coset space
- T-duality
- phase space
References(89)
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