Abstracts
Branislav Sazdovic
The field strength of nongeometric theories
In order to enable open string invariance at string endpoints under: local gauge transformations of the KalbRamond field and its Tdual general coordinate transformations, we added new terms in the action with Neumann and Dirichlet vector gauge fields.
Performing generalized Tdualization of the vector gauge fields linear in coordinates, we will obtain nonlocal and hence locally nongeometric theory. The same theory can be described as a theory with constant field strength and then we can perform standard Buscher Tdualization. These two approaches lead to the relation between Tdual gauge fields of nongeometric theory and Tdual field strength of geometric theory.
The connection between them is nonstandard for two reasons. First, because we must use derivatives of vector fields with respect not only to the Tdual variable $y_\mu$ but also to its double ${\tilde y}_\mu$, which is source of nonlocality. Second, because the Tdual field strength contains both antisymmetric and symmetric parts. Consequently, with the help of Tduality we are able to introduce the field strength in terms of gauge fields for nongeometric theories.
All above results can be interpreted as coordinate permutations in double space. So, in the open string case complete set of Tduality transformations form the same subgroup of the 2D permutation group as in the closed string case.
