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N=1 Mirror Symmetry and Open/Closed String Duality

P. Mayr
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Abstract

We show that the exact N=1 superpotential of a class of 4d string compactifications is computed by the closed topological string compactified to two dimensions. A relation to the open topological string is used to define a special geometry for N=1 mirror symmetry. Flat coordinates, an N=1 mirror map for chiral multiplets and the exact instanton corrected superpotential are obtained from the periods of a system of differential equations. The result points to a new class of open/closed string dualities which map individual string world-sheets with boundary to ones without. It predicts an mathematically unexpected coincidence of the closed string Gromov-Witten invariants of one Calabi-Yau geometry with the open string invariants of the dual Calabi-Yau.

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P. Mayr. 2001-11-13. N=1 Mirror Symmetry and Open/Closed String Duality. https://arxiv.org/abs/hep-th/0108229

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