Communications in Number Theory and Physics

Volume 1 (2007)

Number 4

Membrane instantons from mirror symmetry

Pages: 681 – 711

DOI: http://dx.doi.org/10.4310/CNTP.2007.v1.n4.a3

Authors

Daniel Robles-Llana (Institute for Theoretical Physics and Spinoza Institute, Utrecht University, The Netherlands)

Frank Saueressig (Institute for Theoretical Physics and Spinoza Institute, Utrecht University, The Netherlands)

Ulrich Theis (Institute for Theoretical Physics Friedrich-Schiller-University, Jena, Germany)

Stefan Vandoren (Institute for Theoretical Physics and Spinoza Institute, Utrecht University, The Netherlands)

Abstract

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.

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