Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. The tension of the domainwall between the two vacua on the brane, which is the generating function for the open GromovWitten invariants, satisfies a certain extension of the Picard-Fuchs differential equation governing periods of the mirror quintic. We verify consistency of the monodromies under analytic continuation of the superpotential over the entire moduli space. We reproduce the first few instanton numbers by a localization computation directly in the A-model, and check Ooguri-Vafa integrality. This is the first exact result on open string mirror symmetry for a compact Calabi-Yau manifold.
Universal formulas for the boundary and crosscap coefficients are presented, which are valid for all symmetric simple current modifications of the charge conjugation invariant of any rational conformal field theory.
We explain the B-model origin of extended Picard-Fuchs equations satisfied by the D-brane superpotential on compact Calabi-Yau threefolds. The domainwall tension is identified with a Poincaré normal function -a transversal holomorphic section of the Griffiths intermediate Jacobian -via the Abel-Jacobi map. Within this formalism, we derive the extended Picard-Fuchs equation associated with the mirror of the real quintic.
Type II orientifolds based on Landau-Ginzburg models are used to describe moduli stabilization for flux compactifications of type II theories from the world-sheet CFT point of view. We show that for certain types of type IIB orientifolds which have no Kähler moduli and are therefore intrinsically non-geometric, all moduli can be explicitly stabilized in terms of fluxes. The resulting four-dimensional theories can describe Minkowski as well as Anti-de-Sitter vacua. This construction provides the first string vacuum with all moduli frozen and leading to a 4D Minkowski background.
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