T-duality as coordinates permutation in double space for weakly curved background

Abstract

In the paper [1] we showed that in double space, where all initial coordinates $x^{\mu }$ are doubled $x^{\mu }\to y_{\mu }$, the T-duality transformations can be performed by exchanging places of some coordinates $x^a$ and corresponding dual coordinates $y_a$. Here we generalize this result to the case of weakly curved background where in addition to the extended coordinate we will also transform extended argument of background fields with the same operator ${\hat{\mathcal{T}}}^a$. So, in the weakly curved background T-duality leads to the physically equivalent theory and complete set of T-duality transformations form the same group as in the flat background. Therefore, the double space represent all T-dual theories in unified manner.

39 pages. Subsections 4.1-4.3 have been changed; Section 5. "Dilaton" and Section 6. "Example: Three torus" have been added

References in corpus (6)

• Double Field Theory
• Doubled Geometry and T-Folds
• The gauge algebra of double field theory and Courant brackets
• T-duality and closed string non-commutative (doubled) geometry
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• T-duality as coordinates permutation in double space

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• Directly from $H$-flux to the family of three nonlocal $R$-flux theories
• Twisted C-brackets
• From geometry to non-geometry via T-duality
• Advantage of the second-order formalism in double space T-dualization of type II superstring
• Double space T-dualization and coordinate dependent RR