Abstract
The role of double space is essential in the new interpretation of T-duality and consequently in an attempt to construct M-theory. The case of the open string is missing in such an approach because until now there has been no appropriate formulation of open string T-duality. In the previous paper (Sazdović, From geometry to non-geometry via T-duality, arXiv:1606.01938, 2017), we showed how to introduce vector gauge fields A^N_a and A^D_i at the end-points of an open string in order to enable open string invariance under local gauge transformations of the Kalb–Ramond field and its T-dual “restricted general coordinate transformations”. We demonstrated that gauge fields A^N_a and A^D_i are T-dual to each other. In the present article we prove that all above results can be interpreted as coordinate permutations in double space.
Highlights
It is well known that M-theory unifies all five consistent superstring theories by a web of T and S dualities
In the present article we extend the interpretation of T-duality in double space to the case of an open string
In string theory the gauge fields appear at the boundary of the open string
Summary
It is well known that M-theory unifies all five consistent superstring theories by a web of T and S dualities. It contains the initial and all corresponding T-dual theories Realization of such a program for T-duality in the bosonic case has been done: for a flat background in Ref. The remaining step is to extend interpretation of T-duality in double space (which we earlier proposed for the case of the closed string) to the case of the open string, . In order to realize a double space formulation in the open string case we should treat Neumann and Dirichlet vector fields in the same way. This has recently been done in Ref. C (2017) 77:634 gives the same expressions for T-dual vector fields AaD and AiN as those obtained in Ref. [1] with Buscher’s procedure
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