$\mathcal{N}=2$ heterotic string compactifications on orbifolds of $K3\times T^2$

Abstract

We study $\mathcal{N}=2$ compactifications of $E_8\times E_8$ heterotic string theory on orbifolds of $K3\times T^2$ by $g^{\prime }$ which acts as an ${\mathbb{Z}}_N$ automorphism of $K3$ together with a$1/N$ shift on a circle of $T^2$. The orbifold action $g^{\prime }$ corresponds to the $26$ conjugacy classes of the Mathieu group $M_{24}$. We show that for the standard embedding the new supersymmetric index for these compactifications can always be decomposed into the elliptic genus of $K3$ twisted by $g^{\prime }$. The difference in one-loop corrections to the gauge couplings are captured by automorphic forms obtained by the theta lifts of the elliptic genus of $K3$ twisted by $g^{\prime }$. We work out in detail the case for which $g^{\prime }$ belongs to the equivalence class $2B$. We then investigate all the non-standard embeddings for$K3$ realized as a $T^4/{\mathbb{Z}}_{\nu }$ orbifold with $\nu =2,4$ and $g^{\prime }$ the $2A$ involution. We show that for non-standard embeddings the new supersymmetric index as well as the difference in one-loop corrections to the gauge couplings are completely characterized by the instanton numbers of the embeddings together with the difference in number of hypermultiplets and vector multiplets in the spectrum.

arXiv comment45 pages, Mathematica files included in the source

References in corpus (23)

• Exact Results for N=2 Compactifications of Heterotic Strings
• Algebras, BPS States, and Strings
• Counting Dyons in N=4 String Theory
• A New Supersymmetric Index
• Moduli Corrections to Gauge and Gravitational Couplings in four dimensional Superstrings
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• Moduli Corrections to Gravitational Couplings from String loops
• Note on Twisted Elliptic Genus of K3 Surface
• Mathieu twining characters for K3
• Dyon Spectrum in CHL Models
• (0,2) Heterotic Gauge Couplings and their M-Theory Origin
• Product Representation of Dyon Partition Function in CHL Models
• Chains of N=2, D=4 heterotic/type II duals
• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
• Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds
• Merging Heterotic Orbifolds and K3 Compactifications with Line Bundles
• Ising Model and $N=2$ Supersymmetric Theories
• Universality of Gauge Thresholds in Non-Supersymmetric Heterotic Vacua
• Perturbative Couplings and Modular Forms in N=2 String Models with a Wilson Line
• A K3 sigma model with Z_2^8:M_{20} symmetry
• Generalised universality of gauge thresholds in heterotic vacua with and without supersymmetry
• Mathieu Moonshine and N=2 String Compactifications
• Heterotic string on the CHL orbifold of K3

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• On Mathieu moonshine and Gromov-Witten invariants
• Heterotic strings on $(K3\times T^2)/{\mathbb{Z}}_3$ and their dual Calabi-Yau threefolds
• 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