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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: The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions as mentioned in this paper.
Abstract: The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge theory, mirror symmetry of sigma-models, branes, Wilson and 't Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlands program, such as Hecke eigensheaves and D-modules, arise naturally from the physics.

145 citations

Journal ArticleDOI
TL;DR: In this article, the vacuum structure and spectra of two-dimensional gauge theories with = (2,2) supersymmetry are investigated, and the BPS spectrum has two dual descriptions which apply in the Higgs and Coulomb phases of the theory respectively.
Abstract: The vacuum structure and spectra of two-dimensional gauge theories with = (2,2) supersymmetry are investigated. These theories admit a twisted mass term for charged chiral matter multiplets. In the case of a U(1) gauge theory with N chiral multiplets of equal charge, an exact description of the BPS spectrum is obtained for all values of the twisted masses. The BPS spectrum has two dual descriptions which apply in the Higgs and Coulomb phases of the theory respectively. The two descriptions are related by a massive analog of mirror symmetry: the exact mass formula which is given by a one-loop calculation in the Coulomb phase gives predictions for an infinite series of instanton corrections in the Higgs phase. The theory is shown to exhibit many phenomena which are usually associated with = 2 theories in four dimensions. These include BPS-saturated dyons which carry both topological and Noether charges, non-trivial monodromies of the spectrum in the complex parameter space, curves of marginal stability on which BPS states can decay and strongly coupled vacua with massless solitons and dyons.

145 citations

Posted Content
TL;DR: In this paper, the authors considered the topological string partition function of higher-genus curves contained in a Fano surface within a Calabi-Yau and verified the Gromov-Witten predictions.
Abstract: We discuss local mirror symmetry for higher-genus curves. Specifically, we consider the topological string partition function of higher-genus curves contained in a Fano surface within a Calabi-Yau. Our main example is the local P^2 case. The Kodaira-Spencer theory of gravity, tailored to this local geometry, can be solved to compute this partition function. Then, using the results of Gopakumar and Vafa and the local mirror map, the partition function can be rewritten in terms of expansion coefficients, which are found to be integers. We verify, through localization calculations in the A-model, many of these Gromov-Witten predictions. The integrality is a mystery, mathematically speaking. The asymptotic growth (with degree) of the invariants is analyzed. Some suggestions are made towards an enumerative interpretation, following the BPS-state description of Gopakumar and Vafa.

143 citations

Posted Content
TL;DR: In this paper, the degrees of the Noether-Lefschetz divisors in 1-parameter families of K3 surfaces were shown to be Fourier coefficients of an explicitly computed modular form of weight 21/2 and level 8.
Abstract: Noether-Lefschetz divisors in the moduli of K3 surfaces are the loci corresponding to Picard rank at least 2. We relate the degrees of the Noether-Lefschetz divisors in 1-parameter families of K3 surfaces to the Gromov-Witten theory of the 3-fold total space. The reduced K3 theory and the Yau-Zaslow formula play an important role. We use results of Borcherds and Kudla-Millson for O(2,19) lattices to determine the Noether-Lefschetz degrees in classical families of K3 surfaces of degrees 2, 4, 6 and 8. For the quartic K3 surfaces, the Noether-Lefschetz degrees are proven to be the Fourier coefficients of an explicitly computed modular form of weight 21/2 and level 8. The interplay with mirror symmetry is discussed. We close with a conjecture on the Picard ranks of moduli spaces of K3 surfaces.

142 citations

Book
01 Jun 2002
TL;DR: The role of pattern outline in Bilateral Symmetry Detection with Briefly Flashed Dot Patterns was discussed in this article, where it was shown that second-order pattern processing throughout the visual field is the dominant process for symmetry detection.
Abstract: Contents: Part I:Introduction. C.W. Tyler, Human Symmetry Perception. Part II:Empirical Evaluation of Symmetry Perception. J. Wagemans, Detection of Visual Symmetries. P. Wenderoth, The Role of Pattern Outline in Bilateral Symmetry Detection With Briefly Flashed Dot Patterns. K.E. Higgins, A. Arditi, K. Knoblauch, Detection and Identification of Mirror-Image Letter Pairs in Central and Peripheral Vision. P.T. Quinlan, Evidence for the Use of Scene-Based Frames of Reference in Two-Dimensional Shape Recognition. G. Leone, M. Lipshits, J. McIntyre, V. Gurfinkel, Independence of Bilateral Symmetry Detection From a Gravitational Reference Frame. J.P. Szlyk, I. Rock, C.B. Fisher, Level of Processing in the Perception of Symmetrical Forms Viewed From Different Angles. S. Hong, M. Pavel, Determinants of Symmetry Perception. C.W. Tyler, L. Hardage, Mirror Symmetry Detection: Predominance of Second-Order Pattern Processing Throughout the Visual Field. P.J. Passmore, A. Johnston, Human Discrimination of Surface Slant in Fractal and Related Textured Images. Part III:Theoretical Issues in Symmetry Analysis. S.C. Dakin, R.J. Watt, Detection of Bilateral Symmetry Using Spatial Filters. C. Latimer, W. Joung, C. Stevens, Modelling Symmetry Detection With Back-Propagation Networks. M.A. Kurbat, A Network Model for Generating Differential Symmetry Axes of Shapes Via Receptive Fields. I. Rentschler, E. Barth, T. Caelli, C. Zetzsche, M. Juttner, On the Generalization of Symmetry Relations in Visual Pattern Classification. F. Labonte, Y. Shapira, P. Cohen, J. Faubert, A Model for Global Symmetry Detection in Dense Images. H. Zabrodsky, D. Algom, Continuous Symmetry: A Model for Human Figural Perception. Y. Bonneh, D. Reisfeld, Y. Yeshurun, Quantification of Local Symmetry: Application to Texture Discrimination. J.S. Joseph, J.D. Victor, A Continuum of Non-Gaussian Self-Similar Image Ensembles With White Power Spectra. L.L. Kontsevich, Symmetry as a Depth Cue. T. Vetter, T. Poggio, Symmetric 3D Objects Are an Easy Case for 2D Object Recognition. L. Matin, W. Li, Mirror Symmetry and Parallelism: Two Opposite Rules for the Identity Transform in Space Perception and Their Unified Treatment by the Great Circle Model. J.R. Pani, The Generalized Cone in Human Spatial Organization.

141 citations


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