Two-point functions of Neumann-Dirichlet open-string sector moduli

We compute at one loop the two-point functions of massless scalars in the Neumann-Dirichlet open-string sector of the type IIB orientifold compactified on $T^2\times T^4/\mathbb{Z}_2$, when $\mathcal{N}=2$ supersymmetry is spontaneously broken. This is done by evaluating correlation functions of ``boundary-changing vertex operators'' which are analogous to correlators of twist fields for closed strings. We use our results to compute the mass developed at one loop by the moduli fields arising in the Neumann-Dirichlet sector.