Related papers: Real Mirror Symmetry for One-parameter Hypersurfac…
We revisit local mirror symmetry associated with del Pezzo surfaces in Calabi-Yau threefolds in view of five-dimensional N=1 E_N theories compactified on a circle. The mirror partner of singular Calabi-Yau with a shrinking del Pezzo…
We study complex structure monodromies of certain Calabi-Yau fibrations and find evidence that they are mirror to Calabi-Yau manifolds with NS5 brane on a divisor. This gives a simple way to construct mirrors to any Calabi-Yau hypersurface…
We study low-degree curves on one-parameter Calabi-Yau hypersurfaces, and their contribution to the space-time superpotential in a superstring compactification with D-branes. We identify all lines that are invariant under at least one…
We describe the mirror of the Z orbifold as a representation of a class of generalized Calabi-Yau manifolds that can be realized as manifolds of dimension five and seven. Despite their dimension these correspond to superconformal theories…
We study Mirror Symmetry of log Calabi-Yau surfaces. On one hand, we consider the number of ``affine lines'' of each degree in the complement of a smooth cubic in the projective plane. On the other hand, we consider coefficients of a…
We explore the dynamics of magnetized nonsupersymmetric D5-brane configurations on Calabi-Yau orientifolds with fluxes. We show that supergravity D-terms capture supersymmetry breaking effects predicted by more abstract Pi-stability…
We use mirror symmetry to determine and sum up a class of membrane instanton corrections to the hypermultiplet moduli space metric arising in Calabi-Yau threefold compactifications of type IIA strings. These corrections are mirror to the D1…
We perform a Hodge theoretic study of parameter dependent families of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifcations. Starting from a geometric Gauss-Manin connection for B type branes we study the…
Mirror symmetry relates type IIB string theory on a Calabi-Yau 3-fold to type IIA on the mirror CY manifold, whose complex structure and Kaehler moduli spaces are exchanged. We show that the mirror map is a particular case of a more general…
We generalize the known method for explicit construction of mirror pairs of $(2,2)$-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in…
We identify the twisted sectors of a compact simplicial toric variety. We do the same for a generic nondegenerate Calabi-Yau hypersurface of an $n$-dimensional simplicial Fano toric variety and then explicitly compute $h^{1,1}_{orb}$ and…
Studying the mirror symmetry of a Calabi-Yau threefold $X$ of the Reye congruence in $\mP^4$, we conjecture that $X$ has a non-trivial Fourier-Mukai partner $Y$. We construct $Y$ as the double cover of a determinantal quintic in $\mP^4$…
In contrast to the world-sheet of a fundamental string, the world-volume of stacked D-branes carries an Azumaya noncommutative structure ([L-Y1: Sec.\ 2] (D(1))), allowing it to directly serve as a probe into noncommutative target-spaces.…
We compute the contribution of Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds to the metric on the hypermultiplet moduli space in the large volume, weak coupling limit. Our results are in perfect agreement with the…
We describe in detail the space of the two K\"ahler parameters of the Calabi--Yau manifold $\P_4^{(1,1,1,6,9)}[18]$ by exploiting mirror symmetry. The large complex structure limit of the mirror, which corresponds to the classical large…
We calculate the B-model on the mirror pair of $X_{2N-2}(2,2,\cdots,2,1,1)$ , which is an $(N-2)$-dimensional Calabi-Yau manifold and has two marginal operators i.e. $h^{1,1}(X_{2N-2}(2,2,\cdots,2,1,1))=2$. In \cite{nagandjin} we have…
We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly…
We prove the Mirror Conjecture for Calabi-Yau manifolds equipped with a holomorphic symplectic form. Such manifolda are also known as complex manifolds of hyperkaehler type. We obtain that a complex manifold of hyperkaehler type is Mirror…
We propose an extended set of differential operators for local mirror symmetry. If $X$ is Calabi-Yau such that $\dim H_4(X,\Z)=0$, then we show that our operators fully describe mirror symmetry. In the process, a conjecture for intersection…
In this paper, we partially extend recent results of Wan concerning the relationship between the zeta functions of a Calabi-Yau hypersurface and its (singular) mirror variety.