Relative periods and open-string integer invariants for a compact Calabi-Yau hypersurface

In this work we compute relative periods for B-branes, realized in terms of divisors in a compact Calabi-Yau hypersurface, by means of direct integration. Although we exemplify the method of direct integration with a particular Calabi-Yau geometry, the recipe automatically generalizes for divisors in other Calabi-Yau geometries as well. From the calculated relative periods we extract double-logarithmic periods. These periods qualify to describe disk instanton generated N=1 superpotentials of the corresponding compact mirror Calabi-Yau geometry in the large volume regime. Finally we extract the integer invariants encoded in these brane superpotentials.