Heterotic strings on $(K3\times T^2)/\mathbb{Z}_3$ and their dual CalabiYau threefolds
Abstract
In this paper we study compactifications of the ${\cal N}=2$ heterotic $E_8\times E_8$ string on $(K3\times T^2)/\mathbb{Z}_3$ with various gauge backgrounds and calculate the topological couplings in the effective supergravity action that arise from oneloop amplitudes. We then identify candidates for dual type IIA compactifications on CalabiYau threefolds and compare the heterotic results with the corresponding topological string amplitudes. We find that the dual CalabiYau geometries are $K3$ fibrations that are also genus one fibered with threesections. Moreover, we show that the intersection form on the polarization lattice of the $K3$ fibration has to be three times the intersection form on the Narain lattice $\Gamma^{1,1}$.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.09697
 Bibcode:
 2019arXiv191109697B
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry