Membrane instantons from mirror symmetry

Abstract

We use mirror symmetry to determine and sum up a class of membrane instanton corrections to the hypermultiplet moduli space metric arising in Calabi-Yau 3-fold compactifications of type- IIA strings. These corrections are mirror to the D1 and D(-1)- brane instantons on the IIB side and are given explicitly in terms of a single function in projective superspace. The corresponding four-dimensional effective action is completely fixed by the Euler number and the genus zero Gopakumar-Vafa invariants of the mirror Calabi-Yau.