From geometry to non-geometry via T-duality

  • Reconsideration of the T-duality of the open string allows us to introduce some geometric features in non-geometric theories. First, we have found what symmetry is T-dual to the local gauge transformations. It includes transformations of background fields but does not include transformations of the coordinates. According to this we have introduced a new, up to now missing term, with additional gauge field AiD (D denotes components with Dirichlet boundary conditions). It compensates non-fulfilment of the invariance under such transformations on the end-points of an open string, and the standard gauge field AaN (N denotes components with Neumann boundary conditions) compensates non-fulfilment of the gauge invariance. Using a generalized procedure we will perform T-duality of vector fields linear in coordinates. We show that gauge fields AaN and AiD are T-dual to ADa and ANi respectively. We introduce the field strength of T-dual non-geometric theories as derivatives of T-dual gauge fields along both T-dual variable yμ and its double ȳμ. This definition allows us to obtain gauge transformation of non-geometric theories which leaves the T-dual field strength invariant. Therefore, we introduce some new features of non-geometric theories where field strength has both antisymmetric and symmetric parts. This allows us to define new kinds of truly non-geometric theories.
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B. Sazdovi?. From geometry to non-geometry via T-duality[J]. Chinese Physics C, 2018, 42(8): 083106. doi: 10.1088/1674-1137/42/8/083106
B. Sazdovi?. From geometry to non-geometry via T-duality[J]. Chinese Physics C, 2018, 42(8): 083106.  doi: 10.1088/1674-1137/42/8/083106 shu
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Received: 2018-02-12
Revised: 2018-05-24
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    Supported by the Serbian Ministry of Education and Science (171031)

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From geometry to non-geometry via T-duality

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

Abstract: Reconsideration of the T-duality of the open string allows us to introduce some geometric features in non-geometric theories. First, we have found what symmetry is T-dual to the local gauge transformations. It includes transformations of background fields but does not include transformations of the coordinates. According to this we have introduced a new, up to now missing term, with additional gauge field AiD (D denotes components with Dirichlet boundary conditions). It compensates non-fulfilment of the invariance under such transformations on the end-points of an open string, and the standard gauge field AaN (N denotes components with Neumann boundary conditions) compensates non-fulfilment of the gauge invariance. Using a generalized procedure we will perform T-duality of vector fields linear in coordinates. We show that gauge fields AaN and AiD are T-dual to ADa and ANi respectively. We introduce the field strength of T-dual non-geometric theories as derivatives of T-dual gauge fields along both T-dual variable yμ and its double ȳμ. This definition allows us to obtain gauge transformation of non-geometric theories which leaves the T-dual field strength invariant. Therefore, we introduce some new features of non-geometric theories where field strength has both antisymmetric and symmetric parts. This allows us to define new kinds of truly non-geometric theories.

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