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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.


Papers
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Journal ArticleDOI
TL;DR: In this article, the authors give a brief introduction to the natural realization of non-perturbative N = 2 quantum field theories as a low energy limit of classical string theory.
Abstract: In this lecture we give a brief, elementary introduction to the natural realization of non-perturbative N = 2 quantum field theories as a low energy limit of classical string theory. We review the systematic construction of six, five, and four dimensional gauge theories using geometrical data, which provides also the exact, non-perturbative solution via mirror symmetry. This construction has lead to the exact solution of a large class of gravity free gauge theories, including Super Yang Mills (SYM) theories as well as non-conventional quantum field theories without a known Lagrangian description.

34 citations

Posted Content
TL;DR: In this article, the numbers of lines and conics on various hypersurfaces which satisfy certain incidence properties are calculated, and shown to agree with the numbers predicted by Greene, Morrison, and Plesser using mirror symmetry in every instance.
Abstract: Mirror symmetry, a phenomenon in superstring theory, has recently been used to give tentative calculations of several numbers in algebraic geometry. In this paper, the numbers of lines and conics on various hypersurfaces which satisfy certain incidence properties are calculated, and shown to agree with the numbers predicted by Greene, Morrison, and Plesser using mirror symmetry in every instance. This increases the number of verified predictions from 3 to 65. Calculations are performed using the Maple package {\sc schubert} written by Katz and Str{\o}mme.

34 citations

Posted Content
TL;DR: In this article, the authors generalize Abouzaid, Auroux, Efimov, Katzarkov and Orlov's result to other punctured Riemann surfaces and reformulate it in terms of certain noncommutative algebras coming from dimer models.
Abstract: Recently Abouzaid, Auroux, Efimov, Katzarkov and Orlov showed that the wrapped Fukaya Categories of punctured spheres and finite unbranched covers of punctured spheres are derived equivalent to the categories of singularities of a superpotential on certain crepant resolutions of toric 3 dimensional singularities. We generalize this result to other punctured Riemann surfaces and reformulate it in terms of certain noncommutative algebras coming from dimer models. In particular, given any consistent dimer model we can look at a subcategory of noncommutative matrix factorizations and show that this category is $A_\infty$-isomorphic to a subcategory of the wrapped Fukaya category of a punctured Riemann surface. The connection between the dimer model and the punctured Riemann surface then has a nice interpretation in terms of a duality on dimer models.

34 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the partition function of N=(2, 2) gauge theories on the two-sphere which flow to Calabi-Yau sigma models in the infrared computes the exact Kahler potential on the quantum Kahler moduli space of the corresponding Calabi Yau.
Abstract: We prove a recent conjecture that the partition function of N=(2, 2) gauge theories on the two-sphere which flow to Calabi-Yau sigma models in the infrared computes the exact Kahler potential on the quantum Kahler moduli space of the corresponding Calabi-Yau. This establishes the two-sphere partition function as a new method of computation of worldsheet instantons and Gromov-Witten invariants. We also calculate the exact two-sphere partition function for N=(2,2) Landau-Ginzburg models with an arbitrary twisted superpotential W. These results are used to demonstrate that arbitrary abelian gauge theories and their associated mirror Landau-Ginzburg models have identical two-sphere partition functions. We further show that the partition function of non-abelian gauge theories can be rewritten as the partition function of mirror Landau-Ginzburg models.

34 citations

Journal ArticleDOI
TL;DR: In this article, the authors construct two-dimensional gauge theories with N = (4,4) supersymmetry from branes of type IIA string theory by embedding the IIA brane construction into M-theory.

34 citations


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