Abstract
In this paper we study compactifications of the mathcal{N} = 2 heterotic E8× E8 string on (K3 × T2)/ℤ3 with various gauge backgrounds and calculate the topological couplings in the effective supergravity action that arise from one-loop amplitudes. We then identify candidates for dual type IIA compactifications on Calabi-Yau threefolds and compare the heterotic results with the corresponding topological string amplitudes. We find that the dual Calabi-Yau geometries are K3 fibrations that are also genus one fibered with three- sections. Moreover, we show that the intersection form on the polarization lattice of the K3 fibration has to be three times the intersection form on the Narain lattice Γ1,1.
Highlights
Calculated for various compactifications with standard embedding of the spin connection into the gauge connection on (K3 × T 2)/ZN and some non-standard embeddings when N = 2 [6]
In this paper we study compactifications of the N = 2 heterotic E8 × E8 string on (K3 × T 2)/Z3 with various gauge backgrounds and calculate the topological couplings in the effective supergravity action that arise from one-loop amplitudes
In this paper we extend the calculation of the new supersymmetric index to compactifications on (K3 × T 2)/Z3 with non-standard embeddings and predict the geometric data of the dual Calabi-Yau manifold
Summary
We compute the massless spectrum as well as the new supersymmetric index for compactifications of the heterotic E8 × E8 string on (K3 × T 2)/Z3. While r = 1, 2 and rk := rk mod 3 This result was essentially bootstrapped in [16] and we reproduce it by directly evaluating the trace after taking a T 4/Z3 orbifold limit of the K3. It encodes the new supersymmetric index for compactifications on (K3 × T 2)/Z3 with standard embedding, as predicted in [17]. We compute the new supersymmetric index of the heterotic theory compactified with standard embedding, where one of the E8 groups remains unbroken. In each case of standard or non-standard embedding we can show that the difference between the number of hypermultiplets and vectormultiplets Nh − Nv computed from the new supersymmetric index matches with the result obtained from explicitly counting the degrees of freedom
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