A class of N=1 dual string pairs and its modular superpotential

We compare the N = 1 F theory compactification of Donagi, Grassi and Witten with modular superpotential - and some closely related models - to dual heterotic models. We read of the F theory spectrum from the cohomology of the fourfold and discuss on the heterotic side the gauge bundle moduli sector (including the spectral surface) and the necessary fivebranes. Then we consider the N = 1 superpotential and show how a heterotic superpotential matching the F theory computation is built up by world sheet instantons. Finally we discuss how the original modular superpotential should be corrected by an additional modular correction factor, which on the F theory side matches nicely with a "curve counting function" for the del Pezzo surface. On the heterotic side we derive the same factor demanding correct T duality transformation properties of the superpotential.