Closed superstring moduli tree-level two-point scattering amplitudes in Type IIB orientifold on $T^6/(Z_2\times Z_2)$

Understand

We reconsider the two-point string scattering amplitudes of massless Neveu-Schwarz--Neveu-Schwarz states of Type IIB orientifold superstring theory on the disk and projective plane in ten dimensions and analyse its $\alpha'$ expansion.

• We also discuss the unoriented Type IIB theory on $T^6/\mathbb{Z}_2\times\mathbb{Z}_2$ where two-point string scattering amplitudes of the complex K\"ahler moduli and complex structures of the untwisted sector are computed on the disk and projective plane.
• New results are obtained together with known ones.
• Finally, we compare string scattering amplitudes results at $\alpha'^2$-order with the (curvature)$^2$ terms in the low energy effective action of D-branes and $\Omega$-planes in both cases.