T-duality of a bosonic string in a weakly curved space-time

Abstract

In this article we consider T-dualization of a $3D$ closed bosonic string that is propagating in space-time metric that has infinitesimal linear dependence on the coordinates $x^{\mu }$. Other fields, Kalb-Ramond and dilaton fields are set to zero. Action with this configuration of fields is not invariant to translations. In order to find T-dual theory we will employ generalization of the Buscher procedure that can be applied to such cases where we have coordinate dependent fields that do not possess translational isometry. Finally, using transformation laws that connect coordinates of starting and T-dual theories, we will be able to examine the geometric structure of T-dual theory.

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• T-duality and closed string non-commutative (doubled) geometry
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• A bi-invariant Einstein-Hilbert action for the non-geometric string
• Gauge symmetries decrease the number of Dp-brane dimensions
• Courant bracket as T-dual invariant extension of Lie bracket
• Twisted C-brackets