Abstract
Bosonic string moving in coordinate dependent background fields is considered. We calculate the generalized currents Poisson bracket algebra and find that it gives rise to the Courant bracket, twisted by a 2-form 2B_{mu nu }. Furthermore, we consider the T-dual generalized currents and obtain their Poisson bracket algebra. It gives rise to the Roytenberg bracket, equivalent to the Courant bracket twisted by a bi-vector Pi ^{mu nu }, in case of Pi ^{mu nu } = 2 {^star B}^{mu nu } = kappa theta ^{mu nu }. We conclude that the twisted Courant and Roytenberg brackets are T-dual, when the quantities used for their deformations are mutually T-dual.
Highlights
Non-geometric backgrounds [1,2,3] include various dualities
Tduality [4,5] is a symmetry between two theories corresponding to different geometries and topologies
The Courant bracket [6,7] is the generalization of the Lie bracket so that it includes both vectors and 1-forms
Summary
Non-geometric backgrounds [1,2,3] include various dualities. Duality symmetry is a way to show the equivalence between two apparently different theories. The Courant bracket [6,7] is the generalization of the Lie bracket so that it includes both vectors and 1-forms It is a fundamental structure of the generalized complex geometry. The self T-duality interchanges momenta with coordinate derivatives, as well as the background fields with their T-dual background fields Another set of generalized currents, T-dual to the aforementioned ones, are constructed and their algebra obtained. We find that their algebra gives rise to the Roytenberg bracket obtained by twisting the Courant bracket by the T-dual of the Kalb–Ramond field. We show that the twisted Courant bracket is T-dual to the corresponding Roytenberg one, obtaining the relation that connects the mathematically relevant structures with the T-duality.
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