Open string T-duality in double space

Abstract

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 $$A^N_a$$ A a N and $$A^D_i$$ A i D 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 $$A^N_a$$ A a N and $$A^D_i$$ A i D 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.