## 10th MATHEMATICAL PHYSICS MEETING: School and Conference on Modern Mathematical Physics

### 9 - 14 September 2019, Belgrade, Serbia

E-mail: mphys10@ipb.ac.rs

### Abstracts

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.

Organizers:

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

Co-organizers:

Serbian Academy of Sciences and Arts (SASA)

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

Faculty of Physics (University of Belgrade)