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

TL;DR

The paper demonstrates that in unoriented string theory, the effective Kalb-Ramond field can depend on T-dual coordinates, making it nontrivial and challenging previous assumptions about its vanishing.

Contribution

It reveals that the effective Kalb-Ramond field depends on T-dual coordinates, showing nontrivial effects in unoriented string theories with weakly curved backgrounds.

Findings

Effective Kalb-Ramond field depends on T-dual coordinate 

Standard proof of vanishing of the field is invalidated

Identified the effective field with the torsion potential

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 $B^{eff}_{\mu\nu}$, 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.