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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: In this article, the Picard-Fuchs equations coincide with the expected Calabi-Yau equations and the mirror families of F.Tonoli's degree 13 Calabi Yau threefold and three of the new CalabiYau threefolds.
Abstract: The aim of this article is to report on recent progress in understanding mirror symmetry for some non-complete intersection Calabi-Yau threefolds. We first construct four new smooth non-complete intersection Calabi-Yau threefolds with h^{1,1}=1, whose existence was previously conjectured by C. van Enckevort and D. van Straten. We then compute the period integrals of candidate mirror families of F. Tonoli's degree 13 Calabi-Yau threefold and three of the new Calabi-Yau threefolds. The Picard-Fuchs equations coincide with the expected Calabi-Yau equations. Some of the mirror families turn out to have two maximally unipotent monodromy points.

25 citations

Journal ArticleDOI
TL;DR: In this article, supersymmetric indices are used to test mirror symmetry of three-dimensional (3D) = 4$ gauge theories and dualities of half-Bogomol'ny Prasad Sommerfield enriched boundary conditions and interfaces in four-dimensional super Yang-Mills theory.
Abstract: We compute supersymmetric indices to test mirror symmetry of three-dimensional (3D) $\mathcal{N}=4$ gauge theories and dualities of half-Bogomol'ny Prasad Sommerfield enriched boundary conditions and interfaces in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory. We find the matching of indices as strong evidences for various dualities of the 3D interfaces conjectured by Gaiotto and Witten under the action of S-duality in Type IIB string theory.

25 citations

Journal ArticleDOI
TL;DR: In this paper, the authors developed a mathematical framework for the computation of open orbifold Gromov-Witten invariants and provided extensive checks with predictions from open string mirror symmetry.
Abstract: We develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of $${[\mathbb{C}^3/\mathbb{Z}_n]}$$ and provide extensive checks with predictions from open string mirror symmetry. To this aim, we set up a computation of open string invariants in the spirit of Katz-Liu [23], defining them by localization. The orbifold is viewed as an open chart of a global quotient of the resolved conifold, and the Lagrangian as the fixed locus of an appropriate anti-holomorphic involution. We consider two main applications of the formalism. After warming up with the simpler example of $${[\mathbb{C}^3/\mathbb{Z}_3]}$$ , where we verify physical predictions of Bouchard, Klemm, Marino and Pasquetti [4,5], the main object of our study is the richer case of $${[\mathbb{C}^3/\mathbb{Z}_4]}$$ , where two different choices are allowed for the Lagrangian. For one choice, we make numerical checks to confirm the B-model predictions; for the other, we prove a mirror theorem for orbifold disc invariants, match a large number of annulus invariants, and give mirror symmetry predictions for open string invariants of genus ≤ 2.

25 citations

Journal ArticleDOI
TL;DR: In this paper, the Saito-Givental theory of a simple elliptic singularity is shown to be mirror to either the Gromov-Witten theory of an elliptic orbifold or the Fan-Jarvis-Ruan-Wenn theory of invertible simple singularity with diagonal symmetries.
Abstract: A simple elliptic singularity of type $E_N^{(1,1)}$ ($N=6,7,8$) can be described in terms of a marginal deformation of an invertible polynomial $W$. In the papers \cite{KS} and \cite{MR} the authors proved a mirror symmetry statement for some particular choices of $W$ and used it to prove quasi-modularity of Gromov-Witten invariants for certain elliptic orbifold $\mathbb{P}^1$s. However, the choice of the polynomial $W$ and its marginal deformation $\phi_{\mu}$ are not unique. In this paper, we investigate the global mirror symmetry phenomenon for the one-parameter family $W+\sigma\phi_{\mu}$. In each case the mirror symmetry is governed by a certain system of hypergeometric equations. We conjecture that the Saito-Givental theory of $W+\sigma\phi_{\mu}$ at any special limit $\sigma$ is mirror to either the Gromov-Witten theory of an elliptic orbifold $\mathbb{P}^1$ or the Fan-Jarvis-Ruan-Witten theory of an invertible simple elliptic singularity with diagonal symmetries, and the limits are classified by the Milnor number of the singularity and the $j$-invariant at the special limit. We prove the conjecture when $W$ is a Fermat polynomial. We also prove that the conjecture is true at the Gepner point $\sigma=0$ in all other cases.

25 citations

Posted ContentDOI
TL;DR: In this article, it was shown that for a quasi-homogeneous polynomial W and an admissible group G within the class, the Frobenius algebra arising in the FJRW theory of [W/G] is isomorphic to the orbifolded Milnor ring of W^T/G^T.
Abstract: 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. Specifically, we show that for a quasi-homogeneous polynomial W and an admissible group G within the class, the Frobenius algebra arising in the FJRW theory of [W/G] is isomorphic (as a Frobenius algebra) to the orbifolded Milnor ring of [W^T/G^T], associated to the dual polynomial W^T and dual group G^T.

25 citations


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