N=1 Mirror Symmetry and Open/Closed String Duality

Details N=1 Mirror Symmetry and Open/Closed String Duality N=1 Mirror Symmetry and Open/Closed String Duality

2001-08-30

arxiv.org/abs/hep-th/0108229v2

Adv.Theor.Math.Phys.5:213-242,2002

Physics

High Energy Physics

High Energy Physics - Theory

harvmac, 29 pages (b), 3 figures; v2: references added

Scientific paper

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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