$ \mathcal{N} $ = 2 higher-derivative couplings from strings

Abstract : We consider the Calabi-Yau reduction of the Type IIA eight derivative one-loop stringy corrections focusing on the couplings of the four dimensional gravity multiplet with vector multiplets and a tensor multiplet containing the NS two-form. We obtain a variety of higher derivative invariants generalising the one-loop topological string coupling, $F_1$, controlled by the lowest order Kahler potential and two new non-topological quantities built out of the Calabi-Yau Riemann curvature.