T-dualization in a curved background in absence of a global symmetry

Abstract

We investigate T-duality of a closed string moving in a weakly curved background of the second order. A previously discussed weakly curved background consisted of a flat metric and a linearly coordinate dependent Kalb-Ramond field with an infinitesimal strength. The background here considered differs from the above in a coordinate dependent metric of the second order. Consequently, the corresponding Ricci tensor is nonzero. As this background does not posses the global shift symmetry the generalized Buscher T-dualization procedure is not applicable to it. We redefine it and make it applicable to backgrounds without the global symmetry.

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• Courant bracket found out to be T-dual to Roytenberg bracket
• Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field
• From geometry to non-geometry via T-duality
• Advantage of the second-order formalism in double space T-dualization of type II superstring
• Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field -- the general case
• Open string T-duality in a weakly curved background
• T-duality of a bosonic string in a weakly curved space-time