On current algebras, generalised fluxes and non-geometry

Abstract

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.

49 pages, v2: typos corrected, references added, new result showing the connection of strong constraint and associativity of current algebra in sections 4.3 and 5.2