Mathcal{N} =2 heterotic string compactifications on orbifolds of K3 \xd7 T2

Abstract

We study mathcal{N} = 2 compactifications of E8 × E8 heterotic string theory on orbifolds of K3 × T2 by g′ which acts as an {mathbb{Z}}_N automorphism of K3 together with a 1/N shift on a circle of T2. The orbifold action g′ corresponds to the 26 conjugacy classes of the Mathieu group M24. 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′. 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′. We work out in detail the case for which g′ 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 ν = 2,4 and g′ 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.