T-duality in the weakly curved background

Abstract

We consider the closed string propagating in the weakly curved background which consists of constant metric and Kalb-Ramond field with infinitesimally small coordinate dependent part. We propose the procedure for constructing the T-dual theory, performing T-duality transformations along coordinates on which the Kalb-Ramond field depends. The obtained theory is defined in the non-geometric double space, described by the Lagrange multiplier $y_{\mu }$ and its $T$-dual ${\tilde{y}}_{\mu }$. We apply the proposed T-duality procedure to the T-dual theory and obtain the initial one. We discuss the standard relations between T-dual theories that the equations of motion and momenta modes of one theory are the Bianchi identities and the winding modes of the other.

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• Fermionic T-duality in fermionic double space
• Courant bracket found out to be T-dual to Roytenberg bracket
• Twisted C-brackets
• From geometry to non-geometry via T-duality
• Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field
• Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field -- the general case
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• Effective theories of two T-dual theories are also T-dual
• Double space T-dualization and coordinate dependent RR