T-dual-coordinate dependence makes the effective Kalb-Ramond field nontrivial

Abstract

We show that the fact that the string theory is unoriented does not necessarily force the Kalb-Ramond field to vanish. We investigated the theory of the open string propagating in the weakly curved background. The effective Kalb-Ramond field $B_{\mu \nu }^{eff}$, the background field of the effective theory obtained on the solution of the boundary conditions, does not depend on the $\Omega$-even effective coordinate $q$, but on its T-dual $\tilde{q}$ which is $\Omega$-odd. This brakes the standard proof that the term with $B_{\mu \nu }^{eff}$ should vanish. From the world-sheet equations of motion we identify $B_{\mu \nu }^{eff}$ with the torsion potential.

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• Non-commutativity parameters depend not only on the effective coordinate but on its T-dual as well