Abstract
We consider a theory of an open string moving in a weakly curved background, composed of a constant metric and a linearly coordinate dependent Kalb-Ramond field with an infinitesimal field strength. We find its T-dual using the generalized Buscher procedure developed for the closed string moving in a weakly curved background, and the fact that solving the boundary conditions, the open string theory transforms to the effective closed string theory. So, T-dualizing the effective theory along all effective directions we obtain its T-dual theory and resume the open sting theory which has such an effective theory. In this way we obtain the open string theory T-dual.
Highlights
T-duality is a symmetry of a string spectrum, exchanging the momentum and the winding numbers, a symmetry which was not encountered in any point particle theory [1,2,3,4], a symmetry which is naturally assumed to be connected with the fact that the strings unlike the point particles can wrap around compactified dimensions [5,6,7]
The effective theory is defined on the doubled space, with a double coordinate appearing in a solution of the boundary conditions
We started with the open string described by coordinates xμ, solved the boundary conditions and obtained the effective string described by the even part of the initial coordinates qμ, we T-dualized the effective theory and obtained the T-dual string described by coordinates μ
Summary
T-duality (reviewed in [1,2]) is a symmetry of a string spectrum, exchanging the momentum and the winding numbers, a symmetry which was not encountered in any point particle theory [1,2,3,4], a symmetry which is naturally assumed to be connected with the fact that the strings unlike the point particles can wrap around compactified dimensions [5,6,7]. The open string T-duality along the isometry directions was investigated using the standard Buscher procedure [15], canonical transformations [15,16], the functional integral approach. We will use the first version of the generalized T-dualization procedure to address the T-duality of an open string moving in the weakly curved background. We will apply the generalized Buscher procedure [20,21,22], developed for the closed string moving in the weakly curved background, to the effective closed string theory, obtained for the solution of the open string boundary conditions, along all effective coordinates. The relations between the initial background and its T-dual differ from those in the closed string case
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