School and Conference on Modern Mathematical Physics

18 - 23 September 2017, Belgrade, Serbia


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Branislav Sazdovic

T-duality and non-geometry

The role of double space is essential in new interpretation of T-duality and consequently in an attempt to construct M-theory. The case of open string is missing in such approach because until now there has been no appropriate formulation of open string T-duality. We will consider here reconsideration of T-duality of the open string. This will allow us to introduce some geometric features in non-geometric theories.

First, we will show that "restricted general coordinate transformations", which includes transformations of background fields but not include transformations of the coordinates, is the symmetry T-dual to the local gauge transformations. This will enable us to introduced new (up to now missing) term in the Lagrangian, with additional gauge field A^D_i (D denotes components with Dirichlet boundary conditions). It compensates non-fulfilment of the invariance under restricted general coordinate transformation on the end-points of open string, as well as standard gauge field A^N_a (N denotes components with Neumann boundary conditions) compensates non-fulfilment of the local gauge invariance on the end-points of open string. Using generalized procedure we will perform T-duality of vector fields linear in coordinates. We show that gauge fields A^N_a and A^D_i are T-dual to *A_D^a and *A_N^i respectively. Finally, we proved that all above results can be interpreted as coordinate permutations in double space.

We introduce the field strength of T-dual non-geometric theories as derivative of T-dual gauge fields along both T-dual variable y_\mu and its double {\tilde y}_\mu. This definition allows us to obtain gauge transformation of non-geometric theories which leaves 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 kind of truly non-geometric theories.


Institute of Physics Belgrade
(University of Belgrade)

Belgrade, Serbia


Mathematical Institute
(Serbian Academy of Sciences and Arts)

Belgrade, Serbia


Faculty of Mathematics
(University of Belgrade)

Belgrade, Serbia

E-mail: mphys9@ipb.ac.rs