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 $\hat {\cal T}^a$. 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.
Highlights
The T-duality is one of the stringy properties, because it has no analogy in particle physics
We proved that T-duality transformations in the double space (2.22), for weakly curved background, unites equations of motion and Bianchi identities
We introduced the extended 2D dimensional space with the coordinates ZM =, which beside initial D dimensional space-time coordinates xμ contains the corresponding T-dual coordinates yμ
Summary
The T-duality is one of the stringy properties, because it has no analogy in particle physics. ◦ Td−1, can be realized by exchanging their places, xa ↔ ya It has been proven for constant background fields, the metric Gμν and the Kalb-Ramond field Bμν , when Buscher’s approach can be applied. This interpretation shows that T-duality leads to the equivalent theory, because replacement of coordinates does not change the physics. We will show that this expression is enough to find background fields from all nodes of the chain (1.1) and T-duality transformations between arbitrary nodes In such a way, as well as in the flat background, we unify all T-dual theories of the chain (1.1).
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