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N=1 Mirror Symmetry and Open/Closed String Duality

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arxiv hep-th/0108229 v2 pith:AVLVNLDG submitted 2001-08-30 hep-th

classification hep-th
keywords stringclosedopenmirrorcalabi-yauclassexactgeometry
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 1 Pith paper

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  1. Hodge-theoretic Open/Closed Correspondence

    math.AG 2025-07 conditional novelty 7.0 of 10

    The relative periods and mixed Hodge structures of an open toric Calabi-Yau 3-orbifold with a brane agree, up to a Tate twist, with the periods and mixed Hodge structures of a closed toric Calabi-Yau 4-orbifold.

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