Topic
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 authors describe the construction of configurations of D6-branes wrapped on compact 3-cycles intersecting at points in non-compact Calabi-Yau threefolds.
Abstract: We describe the construction of configurations of D6-branes wrapped on compact 3-cycles intersecting at points in non-compact Calabi-Yau threefolds. Such constructions provide local models of intersecting brane worlds, and describe sectors of four-dimensional gauge theories with chiral fermions. We present several classes of non-compact manifolds with compact 3-cycles intersecting at points, and discuss the rules required for model building with wrapped D6-branes. The rules to build 3-cycles are simple, and allow easy computation of chiral spectra, RR tadpoles and the amount of preserved supersymmetry. We present several explicit examples of these constructions, some of which have Standard Model like gauge group and three quark-lepton generations. In some cases, mirror symmetry relates the models to other constructions used in phenomenological D-brane model building, like D-branes at singularities. Some simple N=1 supersymmetric configurations may lead to relatively tractable G_2 manifolds upon lift to M-theory, which would be non-compact but nevertheless yield four-dimensional chiral gauge field theories.
82 citations
TL;DR: In this article, it was shown that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following ideas of Witten.
Abstract: We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following ideas of Witten. Moreover, on both sides, we highlight two remarkable integral local systems arising from the common formalism of Gamma-integral structures applied to the derived category of the hypersurface {W=0} and to the category of graded matrix factorizations of W. In this setup, we prove that the analytic continuation matches Orlov equivalence between the two above categories.
82 citations
TL;DR: In this paper, the authors analyze three dimensional gauge theories with Sp gauge group and find that in some regime the theory should be described in terms of a dual theory, very much in the spirit of Seiberg duality in four dimensions.
82 citations
TL;DR: Mirror symmetry of the type II string has a beautiful generalization to the heterotic string as discussed by the authors, known as (0,2) mirror symmetry, is a field still largely in its infancy.
Abstract: Mirror symmetry of the type II string has a beautiful generalization to the heterotic string. This generalization, known as (0,2) mirror symmetry, is a field still largely in its infancy. We describe recent developments including the ideas behind quantum sheaf cohomology, the mirror map for deformations of (2,2) mirrors, the construction of mirror pairs from worldsheet duality, as well as an overview of some of the many open questions. The (0,2) mirrors of Hirzebruch surfaces are presented as a new example.
81 citations
TL;DR: By applying mirror symmetry to D-branes in a Calabi-Yau geometry, this paper shed light on a G2 flop in M-theory relevant for large N dualities in = 1 supersymmetric gauge theories.
Abstract: By applying mirror symmetry to D-branes in a Calabi-Yau geometry we shed light on a G2 flop in M-theory relevant for large N dualities in = 1 supersymmetric gauge theories. Furthermore, we derive superpotential for M-theory on corresponding G2 manifolds for all A-D-E cases. This provides an effective method for geometric engineering of = 1 gauge theories for which mirror symmetry gives exact information about vacuum geometry. We also find a number of interesting dual descriptions.
81 citations