Heterotic strings on (K3 × T2)/ℤ3 and their dual Calabi-Yau threefolds

A bstract In this paper we study compactifications of the N = 2 heterotic E 8 × E 8 string on ( K 3 × T 2 )/ℤ 3 with various gauge backgrounds and calculate the topological couplings in the effective supergravity action that arise from one-loop amplitudes. We then identify candidates for dual type IIA compactifications on Calabi-Yau threefolds and compare the heterotic results with the corresponding topological string amplitudes. We find that the dual Calabi-Yau geometries are K 3 fibrations that are also genus one fibered with three- sections. Moreover, we show that the intersection form on the polarization lattice of the K 3 fibration has to be three times the intersection form on the Narain lattice Γ 1 , 1 .