Heterotic string on the CHL orbifold of K3

Abstract

We study $\mathcal{N}=2$ compactifications of heterotic string theory on the CHL orbifold $(K3\times T^2)/{\mathbb{Z}}_N$ with $N=2,3,5,7$. ${\mathbb{Z}}_N$ acts as an involution 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 $K3\times T^2$ studied in the context of dualities in $\mathcal{N}=2$ string theories. We evaluate the new supersymmetric index for these theories and show that their expansion can written in terms of the McKay-Thompson series associated with the ${\mathbb{Z}}_N$ involution 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 $\mathcal{N}=4$ string theories.

46 pages

References in corpus (9)

• Notes on the K3 Surface and the Mathieu group M_24
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• Note on Twisted Elliptic Genus of K3 Surface
• Product Representation of Dyon Partition Function in CHL Models
• Dyon Spectrum in N=4 Supersymmetric Type II String Theories
• Mathieu Moonshine in the elliptic genus of K3
• Universality of Gauge Thresholds in Non-Supersymmetric Heterotic Vacua
• Generalised universality of gauge thresholds in heterotic vacua with and without supersymmetry
• Threshold corrections, generalised prepotentials and Eichler integrals

Cited by in corpus (9)

• Dyon degeneracies from Mathieu moonshine
• $\mathcal{N}=2$ heterotic string compactifications on orbifolds of $K3\times T^2$
• Threshold corrections in heterotic flux compactifications
• Gravitational couplings in $\mathcal{N}=2$ string compactifications and Mathieu Moonshine
• On Mathieu moonshine and Gromov-Witten invariants
• Calabi-Yau manifolds and sporadic groups
• Gravitational couplings in $\mathcal{N}=2$ heterotic compactifications with Wilson lines
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• Moduli spaces of non-geometric type II/heterotic dual pairs