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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: For the moduli space of strongly parabolic Higgs bundles of rank two and three, with full flags, for any generic weights, the authors proved the topological mirror symmetry conjecture of Hausel and Thaddeus.
18 citations
TL;DR: In this article, the first forbidden beta-decay of 17Ne into the 'halo' state J = 1/2+ of 17F was studied in the framework of the Shell Model Embedded in the Continuum.
Abstract: The first-forbidden beta-decay of 17Ne into the 'halo' state J=1/2+ of 17F presents one of the largest measured asymmetries for mirror beta-decay feeding bound final states. This asymmetry is studied in the framework of the Shell Model Embedded in the Continuum (SMEC). The spatial extent of single particle orbits is constrained by the proton capture cross-section 16O(p,gamma)17F calculated in SMEC . This allows to estimate the mirror symmetry breaking in 17F/17O and 17Ne/17N nuclei.
18 citations
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TL;DR: In this article, a Floer-theoretic torsion invariant I_F was introduced, which roughly takes the form of a product of a power series counting perturbed pseudo-holomorphic tori, and the Reidemeister torsions of the symplectic Floer complex.
Abstract: In a previous paper, the author introduced a Floer-theoretic torsion invariant I_F, which roughly takes the form of a product of a power series counting perturbed pseudo-holomorphic tori, and the Reidemeister torsion of the symplectic Floer complex. We pointed out the formal resemblance of I_F with a generating function of genus 1 Gromov invariant; furthermore, for heuristic reasons one also expects a relation with the 1-loop generating function in the A-model side of mirror symmetry, which counts genus 1 holomorphic curves.
The present article makes this expected relation precise in the simplest cases, in two variants of the I_F defined in the earlier work: the lagrangian intersection version, I_F(L, L'), and an S^1-equivariant version, I_F^{S^1}.
As a by-product, we obtain some existence results of noncontractible periodic orbits in symplectic dynamics. For example, the results of Gatien-Lalonde are extended to a much wider class of manifolds.
The two versions I_F(L, L') and I_F^{S^1} are only minimally developed in this paper, leaving fuller accounts to future work. The lagrangian intersection version, I_F(L, L'), should be viewed as a simplest example of a rigorous definition of the higher-loop ``open Gromov-Witten invariants'' proposed by physicists.
18 citations
TL;DR: In this article, the authors studied the topology of certain K3 surfaces equipped with certain Kahler forms and proved that the Torelli group may be infinitely generated, and derived new constraints on Lagrangian tori.
Abstract: We study the symplectic topology of certain K3 surfaces (including the "mirror quartic" and "mirror double plane"), equipped with certain Kahler forms. In particular, we prove that the symplectic Torelli group may be infinitely generated, and derive new constraints on Lagrangian tori. The key input, via homological mirror symmetry, is a result of Bayer and Bridgeland on the autoequivalence group of the derived category of an algebraic K3 surface of Picard rank one.
18 citations
TL;DR: In this paper, a relationist will account for the use of "left" and "right" in terms of relative orientations, and other properties and relations invariant under mirroring.
Abstract: A relationist will account for the use of ‘left’ and ‘right’ in terms of relative orientations, and other properties and relations invariant under mirroring. This analysis will apply whenever mirroring is a symmetry, so it certainly applies to classical mechanics; we argue it applies to any physical theory formulated on a manifold: it is in this sense an a priori symmetry. It should apply in particular to parity violating theories in quantum mechanics; mirror symmetry is only broken in such theories as a special symmetry.
18 citations