an:01807476
Zbl 1022.81046
Mayr, P.
\(N=1\) mirror symmetry and open/closed string duality
EN
Adv. Theor. Math. Phys. 5, No. 2, 213-242 (2001).
00086794
2001
j
81T30 83E30 32Q25 14N35
topological string compactified to two dimensions; Gromov-Witten invariants; Calabi-Yau geometry
Summary: We show that the exact \({\mathcal N}= 1\) superpotential of a class of four-dimensional 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 \({\mathcal N}= 1\) mirror symmetry. Flat coordinates, an \({\mathcal N}= 1\) 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.