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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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Book ChapterDOI
01 Jan 2014
TL;DR: In this paper, the notion of wall-crossing structure and its constructions and applications in various situations are discussed. But the main focus of this paper is on the use of wall crossings in Mirror Symmetry and Donaldson-Thomas invariants.
Abstract: The paper is devoted to the notion of wall-crossing structure and its constructions and applications in various situations. It is motivated by our previous work on Mirror Symmetry and Donaldson–Thomas invariants (see [30, 31, 35, 36]) where examples of wall-crossing structures appeared for the first time.

76 citations

Journal ArticleDOI
TL;DR: In this article, the Ricci-flat Kahler metrics collapse with locally bounded curvature, and along the fibers the rescaled metrics become flat in the limit, where the limit metric on the base minus the critical locus is locally isometric to an open dense subset of any Gromov-Hausdorff limit space.
Abstract: We study the collapsing behavior of Ricci-flat Kahler metrics on a projective Calabi–Yau manifold which admits an abelian fibration, when the volume of the fibers approaches zero. We show that away from the critical locus of the fibration the metrics collapse with locally bounded curvature, and along the fibers the rescaled metrics become flat in the limit. The limit metric on the base minus the critical locus is locally isometric to an open dense subset of any Gromov–Hausdorff limit space of the Ricci-flat metrics. We then apply these results to study metric degenerations of families of polarized hyperkahler manifolds in the large complex structure limit. In this setting, we prove an analogue of a result of Gross and Wilson for K3 surfaces, which is motivated by the Strominger–Yau–Zaslow picture of mirror symmetry.

76 citations

Journal ArticleDOI
TL;DR: In this paper, negative branes are used to generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves.
Abstract: We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3-branes, we show that SU(0|N) supergroup theories are holographically dual to an exotic variant of type IIB string theory on $$ {\mathrm{dS}}_{3,2}\times {\overline{\mathrm{S}}}^5 $$ , for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov’s instanton calculus, all of which agree, we derive the Seiberg-Witten curve for $$ \mathcal{N}=2 $$ SU(N |M ) gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.

76 citations

Journal ArticleDOI
TL;DR: In this paper, a relative version of T -duality in generalized complex geometry is proposed as a manifestation of mirror symmetry, and a bijective correspondence between ∇ -semi-flat generalized almost complex structures on the total space of a real manifold and ∇ ∨ semi-flat GAs on the manifold is established.

76 citations

Journal ArticleDOI
TL;DR: In this paper, the foundations of homological mirror symmetry for manifolds of general type are outlined and both physics and Categorical prospectives are considered, and the results of the analysis are presented.
Abstract: In this paper we outline the foundations of Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical prospectives are considered.

75 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202351
2022116
2021138
2020130
2019139
2018125