A Hamiltonian formulation of the classical world-sheet theory in a generic, geometric or non-geometric, NSNS background is proposed. The essence of this formulation is a deformed current algebra, which is solely characterised by the generalised fluxes describing such a background. The construction extends to backgrounds for which there is no Lagrangian description—namely magnetically charged backgrounds or those violating the strong constraint of double field theory—at the cost of violating the Jacobi identity of the current algebra. The known non-commutative and non-associative interpretation of non-geometric flux backgrounds is reproduced by means of the deformed current algebra. Furthermore, the provided framework is used to suggest a generalisation of Poisson–Lie T -duality to generic models with constant generalised fluxes. As a side note, the relation between Lie and Courant algebroid structures of the string current algebra is clarified.

中文翻译：

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当前代数，广义通量和非几何

提出了在普通的，几何的或非几何的NSNS背景下经典世界表理论的哈密顿公式。该公式的本质是变形的电流代数，其仅由描述这种背景的广义通量来表征。这种构造扩展到了没有拉格朗日描述的背景（即带磁背景或违反双场理论的强约束的背景），但其代价是违反了当前代数的Jacobi身份。非几何通量背景的已知的非交换性和非关联性解释是通过变形的电流代数来再现的。此外，所提供的框架用于建议将Poisson-Lie T-对偶性推广到具有恒定广义通量的通用模型。作为旁注，