Topic
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: In this paper, the topological aspect of UPt3 was investigated through microscopic calculations of edge and vortex-bound states based on the quasiclassical Eilenberger and Bogoliubov-de Gennes theories.
Abstract: We investigate the topological aspect of the spin-triplet f-wave superconductor UPt3 through microscopic calculations of edge- and vortex-bound states based on the quasiclassical Eilenberger and Bogoliubov–de Gennes theories. It is shown that a gapless and linear dispersion exists at the edge of the ab-plane. This forms a Majorana valley, protected by the mirror chiral symmetry. We also demonstrate that, with increasing magnetic field, vortex-bound quasiparticles undergo a topological phase transition from topologically trivial states in the double-core vortex to zero-energy states in the normal-core vortex. As long as the d-vector is locked into the ab-plane, the mirror symmetry holds the Majorana property of the zero-energy states, and thus UPt3 preserves topological crystalline superconductivity that is robust against the crystal field and spin–orbit interaction.
60 citations
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TL;DR: In this paper, a conjecture on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian submanifold of a Calabi-Yau manifold is proposed.
Abstract: Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian submanifold of a Calabi-Yau manifold. It involves a stability condition for graded Lagrangians, and can be proved for the simple case of $T^2$.
60 citations
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TL;DR: In this paper, the authors use Strominger-Yau-Zaslow's geometric approach to mirror symmetry as a torus duality to construct the mirror of a symplectic manifold equipped with a Lagrangian torus fibration as a moduli space of simple objects of the Fukaya category supported on the fibres.
Abstract: Ideas of Fukaya and Kontsevich-Soibelman suggest that one can use Strominger-Yau-Zaslow's geometric approach to mirror symmetry as a torus duality to construct the mirror of a symplectic manifold equipped with a Lagrangian torus fibration as a moduli space of simple objects of the Fukaya category supported on the fibres. In the absence of singular fibres, the construction of the mirror is explained in this framework, and, given a Lagrangian submanifold, a (twisted) coherent sheaf on the mirror is constructed.
60 citations
TL;DR: In this article, the chiral ring may be identical for different associated conformal field theories in terms of both A-model and B-model language, and this ambiguity is explained by both the A-and B-models.
60 citations
TL;DR: In this paper, a detailed analysis of pairs of vector and hypermultiplet theories with N = 2 supersymmetry in four space-time dimensions that are related by the (classical) mirror map is given.
60 citations