{\cal N}=2 heterotic string compactifications on orbifolds of K3×T²

Abstract

We study N = 2 compactifications of E 8 × E 8 heterotic string theory on orbifolds of K3 × T 2 by g ′ which acts as an ZN automorphism of K3 together with a 1/N shift on a circle of T 2. The orbifold action g ′ 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 ′. 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 T4/Zν 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.