Heterotic string on the CHL orbifold of K3

Abstract

We study N=2 compactifications of heterotic string theory on the CHL orbifold (K3×T2)/ZN with N = 2, 3, 5, 7. ZN acts as an automorphism on K3 together with a shift of 1/N along one of the circles of T 2. These compactifications generalize the example of the heterotic string on K3 × T 2 studied in the context of dualities in N=2 string theories. We evaluate the new supersymmetric index for these theories and show that their expansion can be written in terms of the McKay-Thompson series associated with the ZN automorphism embedded in the Mathieu group M 24. We then evaluate the difference in one-loop threshold corrections to the non-Abelian gauge couplings with Wilson lines and show that their moduli dependence is captured by Siegel modular forms related to dyon partition functions of N=4 string theories.