Related papers: Mirror Symmetry Constructions: A Review
We study the realization of the (super) conformal topological symmetry in two-dimensional field theories. The mirror automorphism of the topological algebra is represented as a reflection in the space of fields. As a consequence, a double…
We prove homological mirror symmetry for orbifold log Calabi-Yau surfaces at the large complex structure limit by constructing an abstract Lefschetz fibration associated to each pair $(\mathcal{X},\mathcal{D})$ with $\mathcal{X}$ a…
Strominger-Yau-Zaslow (SYZ) proposed a way of constructing mirror pairs as pairs of torus fibrations. We apply this SYZ construction to toric Fano surfaces as complex manifolds, and discuss the homological mirror symmetry, where we consider…
We prove Kontsevich's homological mirror symmetry conjecture for a large class of mirror pairs of Calabi--Yau hypersurfaces in toric varieties. These mirror pairs were constructed by Batyrev from dual reflexive polytopes. The theorem holds…
We formulate general conjectures about the relationship between the A-model connection on the cohomology of a $d$-dimensional Calabi-Yau complete intersection $V$ of $r$ hypersurfaces $V_1, \ldots, V_r$ in a toric variety ${\bf P}_{\Sigma}$…
Given a Fano complete intersection defined by sections of a collection nef line bundles $L_1,\ldots, L_c$ on a Fano toric manifold $Y$, a construction of Givental/Hori-Vafa provides a mirror-dual Landau-Ginzburg model. This construction…
We formulate some precise conjectures concerning the existence and structure of supersymmetric T3 fibrations of Calabi-Yau threefolds, and describe how these conjectural fibrations would give rise to the Strominger-Yau-Zaslow version of…
The goal of this paper is to propose a theory of mirror symmetry for varieties of general type. Using Landau-Ginzburg mirrors as motivation, we describe the mirror of a hypersurface of general type (and more generally varieties of…
The recent result of Strominger, Yau and Zaslow relating mirror symmetry to the quantum field theory notion of T-duality is reinterpreted as providing a way of geometrically characterizing which Calabi-Yau manifolds have mirror partners.…
We prove the Landau-Ginzburg Mirror Symmetry Conjecture at the level of (orbifolded) Frobenius algebras for a large class of invertible singularities, including arbitrary sums of loops and Fermats with arbitrary symmetry groups.…
In this paper, we prove the mirror symmetry conjecture between the Saito-Givental theory of exceptional unimodular singularities on Landau-Ginzburg B-side and the Fan-Jarvis-Ruan-Witten theory of their mirror partners on Landau-Ginzburg…
When studying mirror symmetry in the context of K3 surfaces, the hyperkaehler structure of K3 makes the notion of exchanging Kaehler and complex moduli ambiguous. On the other hand, the metric is not renormalized due to the higher amount of…
We observe that the state space of Landau-Ginzburg isolated singularities is simply a special case of Chen-Ruan orbifold cohomology relative to the generic fibre of the potential. This leads to the definition of the cohomology of hybrid…
We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization). Our results agree with B-model computations from solutions of Picard-Fuchs differential…
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by…
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…
Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror \hat{M}, it is argued that the product M x \hat{M} is doubly fibered by supersymmetric…
Toroidal 3-orbifolds $(S^1)^6/G$, for $G$ a finite group, were some of the earliest examples of Calabi-Yau 3-orbifolds to be studied in string theory. While much mathematical progress towards the predictions of string theory has been made…
The recent classification of Landau--Ginzburg potentials and their abelian symmetries focuses attention on a number of models with large positive Euler number for which no mirror partner is known. All of these models are related to…
The Strominger-Yau-Zaslow (SYZ) approach to mirror symmetry constructs a mirror space and a superpotential from the data of a Lagrangian torus fibration on a K\"ahler manifold with effective first Chern class. For K\"ahler manifolds whose…