Communications in Number Theory and Physics
Volume 1 (2007)
Membrane instantons from mirror symmetry
Pages: 681 – 711
We use mirror symmetry to determine and sum up a class ofmembrane instanton corrections to the hypermultipletmoduli space metric arising in Calabi–Yau 3-foldcompactifications of type-IIA strings. These corrections are mirrorto the D1 and D($-1$)-brane instantons on the IIB side and are givenexplicitly in terms of a single function in projectivesuperspace. The corresponding four-dimensional effectiveaction is completely fixed by the Euler number and the genus zeroGopakumar–Vafa invariants of the mirror Calabi–Yau.