We discuss the properties of massive type IIA flux compactifications. In particular, we investigate in which case one can obtain dS vacua at large volume and small coupling. We support a general discussion of scaling symmetries with the analysis of a concrete example. We find that the large volume and weak coupling limit requires a large number of O6-planes. Since these are bound for any given compactification space one cannot get arbitrarily good control over α and string loop corrections. arXiv:1811.07880v2 [hep-th]

We provide strong evidence that a large number of CY 3 manifolds are involved in an intricate way in Mathieu moonshine viz. their Gromov-Witten invariants are related to the expansion coefficients of the twined/twisted-twined elliptic genera of K3. We use the conjectured string duality between CHL orbifolds of heterotic string theory on K3 × T 2 and type IIA string theory on CY 3 manifolds to explicitly show this connection. We then work out two concrete examples where we exactly match the expansion coefficients on both sides of the duality.

In this paper we study compactifications of the N = 2 heterotic E 8 × E 8 string on (K3 × T 2 )/Z 3 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 threesections. 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 Γ 1,1 .

A few years ago a connection between the elliptic genus of the K3 manifold and the largest Mathieu group M 24 was proposed. We study the elliptic genera for Calabi-Yau manifolds of larger dimensions and discuss potential connections between the expansion coefficients of these elliptic genera and sporadic groups. While the Calabi-Yau 3-fold case is rather uninteresting, the elliptic genera of certain Calabi-Yau d-folds for d > 3 have expansions that could potentially arise from underlying sporadic symmetry groups. We explore such potential connections by calculating twined elliptic genera for a large number of Calabi-Yau 5-folds that are hypersurfaces in weighted projected spaces, for a toroidal orbifold and two Gepner models.

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