School and Conference on Modern Mathematical Physics

9 - 14 September 2019, Belgrade, Serbia


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    E-mail: mphys10@ipb.ac.rs


Branislav Sazdovic

The field strength of non-geometric theories

In order to enable open string invariance at string end-points under: local gauge transformations of the Kalb-Ramond field and its T-dual general coordinate transformations, we added new terms in the action with Neumann and Dirichlet vector gauge fields.

Performing generalized T-dualization of the vector gauge fields linear in coordinates, we will obtain non-local and hence locally non-geometric theory. The same theory can be described as a theory with constant field strength and then we can perform standard Buscher T-dualization. These two approaches lead to the relation between T-dual gauge fields of non-geometric theory and T-dual field strength of geometric theory.

The connection between them is non-standard for two reasons. First, because we must use derivatives of vector fields with respect not only to the T-dual variable $y_\mu$ but also to its double ${\tilde y}_\mu$, which is source of non-locality. Second, because the T-dual field strength contains both antisymmetric and symmetric parts. Consequently, with the help of T-duality we are able to introduce the field strength in terms of gauge fields for non-geometric theories.

All above results can be interpreted as coordinate permutations in double space. So, in the open string case complete set of T-duality transformations form the same subgroup of the 2D permutation group as in the closed string case.


Institute of Physics Belgrade (University of Belgrade)
Belgrade, Serbia
Faculty of Mathematics (University of Belgrade)
Belgrade, Serbia
Mathematical Institute (Serbian Academy of Sciences and Arts)
Belgrade, Serbia
Faculty of Science (University of Kragujevac)
Kragujevac, Serbia


Serbian Academy of Sciences and Arts (SASA)
Belgrade, Serbia

Institute of Nuclear Sciences "VinĨa" (University of Belgrade)
Belgrade, Serbia
Institute of Physics (University of Kragujevac)
Kragujevac, Serbia

Faculty of Physics (University of Belgrade)
Belgrade, Serbia
Faculty of Sciences (University of Novi Sad)
Novi Sad, Serbia
School of Electrical Engineering (University of Belgrade)
Belgrade, Serbia

SEENET-MTP (Southeastern European Network in Mathematical and Theoretical Physics)
Nis, Serbia