Enhanced supersymmetry from vanishing Euler number

We argue that compactifications on Calabi-Yau threefolds with vanishing Euler number yield effective four dimensional theories exhibiting (spontaneously broken) N=4 supersymmetry. To this end, we derive the low-energy effective action for general SU(2) structure manifolds in type IIA string theory and show its consistency with gauged N=4 supergravity. Focusing on the special case of Calabi-Yau manifolds with vanishing Euler number, we explain the absence of perturbative corrections at the two-derivative level. In addition, we conjecture that all non-perturbative corrections are governed and constrained by the couplings of N=4 massive gravitino multiplets.