T-duality as permutation of coordinates in double space

  • We introduce the 2D dimensional double space with the coordinates ZM= (xμ, yμ), whose components are the coordinates of initial space xμ and its T-dual yμ. We shall show that in this extended space the T-duality transformations can be realized simply by exchanging the places of some coordinates xa, along which we want to perform T-duality, and the corresponding dual coordinates y_a. In such an approach it is evident that T-duality leads to the physically equivalent theory and that a complete set of T-duality transformations forms a subgroup of the 2D permutation group. So, in double space we are able to represent the backgrounds of all T-dual theories in a unified manner.
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B. Sazdovi?. T-duality as permutation of coordinates in double space[J]. Chinese Physics C, 2017, 41(5): 053101. doi: 10.1088/1674-1137/41/5/053101
B. Sazdovi?. T-duality as permutation of coordinates in double space[J]. Chinese Physics C, 2017, 41(5): 053101.  doi: 10.1088/1674-1137/41/5/053101 shu
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Received: 2016-12-09
Revised: 2017-01-23
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T-duality as permutation of coordinates in double space

Fund Project:  Supported by the Serbian Ministry of Education and Science (171031)

Abstract: We introduce the 2D dimensional double space with the coordinates ZM= (xμ, yμ), whose components are the coordinates of initial space xμ and its T-dual yμ. We shall show that in this extended space the T-duality transformations can be realized simply by exchanging the places of some coordinates xa, along which we want to perform T-duality, and the corresponding dual coordinates y_a. In such an approach it is evident that T-duality leads to the physically equivalent theory and that a complete set of T-duality transformations forms a subgroup of the 2D permutation group. So, in double space we are able to represent the backgrounds of all T-dual theories in a unified manner.

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