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Mirror symmetry
About: Mirror symmetry is a research topic. Over the lifetime, 2422 publications have been published within this topic receiving 90786 citations.
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TL;DR: Waleffe et al. as mentioned in this paper obtained two new families of exact coherent states in plane Poiseuille flow by a homotopy continuation of the stationary and the travelling-wave mirror-symmetric solutions in Couette flow.
Abstract: Two new families of exact coherent states are found in plane Poiseuille flow. They are obtained from the stationary and the travelling-wave mirror-symmetric solutions in plane Couette flow by a homotopy continuation. They are characterized by the mirror symmetry inherited from those continued solutions in plane Couette flow. The first family arises from a saddle-node bifurcation and the second family bifurcates by breaking the top–bottom symmetry of the first family. We find that both families exist below the minimum saddle-node-point Reynolds number known to date (Waleffe, Phys. Fluids, vol. 15, 2003, pp. 1517–1534).
34 citations
TL;DR: In this paper, a vertex algebra proof of the Berglund-Hubsch duality of non-degenerate invertible potentials is given, and a way to unify it with the Batyrev-Borisov duality for reflexive Gorenstein cones is proposed.
Abstract: We give a vertex algebra proof of the Berglund-Hubsch duality of nondegenerate invertible potentials. We suggest a way to unify it with the Batyrev-Borisov duality of reflexive Gorenstein cones.
34 citations
TL;DR: Mirror symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed in this article for Calabi-Yau spaces with two and three moduli.
Abstract: Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.
34 citations
TL;DR: In this article, the authors discussed a K3 and torus from view point of mirror symmetry and calculated the periods of the K3 surface and obtained the mirror map, the two-point correlation function, and the prepotential.
Abstract: We discuss a K3 and torus from view point of "mirror symmetry". We calculate the periods of the K3 surface and obtain the mirror map, the two-point correlation function, and the prepotential. Then we find there is no instanton correction on K3 (also torus), which is expected from view point of Algebraic geometry.
34 citations
TL;DR: In this paper, the Hamiltonian dispersionless hierarchies that govern the full descendent genus zero theory of Calabi-Yau rank two bundles over the projective line and the theory of integrable hierarchies are constructed.
Abstract: In this paper we begin the study of the relationship between the local Gromov-Witten theory of Calabi-Yau rank two bundles over the projective line and the theory of integrable hierarchies. We first of all construct explicitly, in a large number of cases, the Hamiltonian dispersionless hierarchies that govern the full descendent genus zero theory. Our main tool is the application of Dubrovin's formalism, based on associativity equations, to the known results on the genus zero theory from local mirror symmetry and localization. The hierarchies we find are apparently new, with the exception of the resolved conifold O(-1) + O(-1) -> P1 in the equivariantly Calabi-Yau case. For this example the relevant dispersionless system turns out to be related to the long-wave limit of the Ablowitz-Ladik lattice. This identification provides us with a complete procedure to reconstruct the dispersive hierarchy which should conjecturally be related to the higher genus theory of the resolved conifold. We give a complete proof of this conjecture for genus g<=1; our methods are based on establishing, analogously to the case of KdV, a "quasi-triviality" property for the Ablowitz-Ladik hierarchy at the leading order of the dispersive expansion. We furthermore provide compelling evidence in favour of the resolved conifold/Ablowitz-Ladik correspondence at higher genus by testing it successfully in the primary sector for g=2.
34 citations