Related papers: A Note on Computations of D-brane Superpotential
Superstring theories are the most promising theories for unified description of all fundamental interactions including gravity. However, these theories are formulated consistently only in 10 spacetime dimensions. Therefore, to connect to…
We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau 3-folds. Along the way we clarify the notion of…
We consider Calabi-Yau compactifications with one K\"ahler modulus. Following the method of Candelas et al. we use the mirror hypothesis to solve the quantum theory exactly in dependence of this modulus by performing the calculation for the…
We review the geometrical framework required for understanding the moduli space of $(2,2)$ superconformal-field theories, highlighting various aspects of its phase structure. In particular, we indicate the types of phase diagrams that…
In this review article we study type IIB superstring compactifications in the presence of space-time filling D-branes while preserving N=1 supersymmetry in the effective four-dimensional theory. This amount of unbroken supersymmetry and the…
A method for computing the open string mirror map and superpotential for noncompact Calabi-Yaus, following the physical computations of Lerche and Mayr, is presented. It is also shown that the obvious extension of these techniques to the…
In this paper we explore contributions to non-perturbative superpotentials arising from instantons wrapping effective divisors in smooth Calabi-Yau four-folds. We concentrate on the case of manifolds constructed as complete intersections in…
We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main…
We present a method for explicitly computing the non-perturbative superpotentials associated with the vector bundle moduli in heterotic superstrings and M-theory. This method is applicable to any stable, holomorphic vector bundle over an…
We study Euclidean D3-branes wrapping divisors $D$ in Calabi-Yau orientifold compactifications of type IIB string theory. Witten's counting of fermion zero modes in terms of the cohomology of the structure sheaf $\mathcal{O}_D$ applies when…
We explain the B-model origin of extended Picard-Fuchs equations satisfied by the D-brane superpotential on compact Calabi-Yau threefolds. Via the Abel-Jacobi map, the domainwall tension is identified with a Poincare normal function--a…
The periods of the three-form on a Calabi-Yau manifold are found as solutions of the Picard-Fuchs equations; however, the toric varietal method leads to a generalized hypergeometric system of equations which has more solutions than just the…
F-theory, as a 12-dimensional theory that is a contender of the Theory of Everything, should be compactified into elliptically fibered threefolds or fourfolds of Calabi-Yau. Such manifolds have an elliptic curve as a fiber, and their bases…
By the modularity theorem every rigid Calabi-Yau threefold $X$ has associated modular form $f$ such that the equality of $L$-functions $L(X,s)=L(f,s)$ holds. In this case period integrals of $X$ are expected to be expressible in terms of…
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…
We extend the discussion of mirror symmetry, Picard-Fuchs equations, instanton-corrected Yukawa couplings, and the topological one-loop partition function to the case of complete intersections with higher-dimensional moduli spaces. We will…
We study the open string extension of the mirror map for N=1 supersymmetric type II vacua with D-branes on non-compact Calabi-Yau manifolds. Its definition is given in terms of a system of differential equations that annihilate certain…
We study periods in an integral basis near all possible singularities in one-dimensional complex structure moduli spaces of Calabi-Yau threefolds. Near large complex structure points these asymptotic periods are well understood in terms of…
The mirror curves enable us to study B-model topological strings on non-compact toric Calabi--Yau threefolds. One of the method to obtain the mirror curves is to calculate the partition function of the topological string with single brane.…
In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of rational curves on complete intersection Calabi-Yau 3-folds…