Nongeometric background arising in the solution of Neumann boundary conditions

Abstract

We investigate the open string propagation in the weakly curved background with the Kalb-Ramond field containing an infinitesimal part, linear in coordinate. Solving the Neumann boundary conditions, we find the expression for the space-time coordinates in terms of the effective ones. So, the initial theory reduces to the effective one. This effective theory is defined on the nongeometric doubled space $(q^μ,\tilde{q}_μ)$, where $q^μ$ is the effective coordinate and $\tilde{q}_μ$ is its T-dual. The effective metric depends on the coordinate $q^μ$ and there exists non-trivial effective Kalb-Ramond field which depends on the T-dual coordinate $\tilde{q}_μ$. The fact that $\tilde{q}_μ$ is $Ω$-odd leads to the nonvanishing effective Kalb-Ramond field.