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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: A good number of theoretical results on symmetries of polynomial curves, algorithms for detecting rotation and mirror symmetry, and closed formulas to determine the symmetry center and the symmetry axis, when they exist are provided.
31 citations
TL;DR: Batyrev as mentioned in this paper showed that many of these missing mirrors may be interpreted as non-transverse hypersurfaces for which dp vanishes at a point other than the origin.
Abstract: Recently two groups have listed all sets of weights (k_1,...,k_5) such that the weighted projective space P_4^{(k_1,...,k_5)} admits a transverse Calabi-Yau hypersurface. It was noticed that the corresponding Calabi-Yau manifolds do not form a mirror symmetric set since some 850 of the 7555 manifolds have Hodge numbers (b_{11},b_{21}) whose mirrors do not occur in the list. By means of Batyrev's construction we have checked that each of the 7555 manifolds does indeed have a mirror. The `missing mirrors' are constructed as hypersurfaces in toric varieties. We show that many of these manifolds may be interpreted as non-transverse hypersurfaces in weighted P_4's, ie, hypersurfaces for which dp vanishes at a point other than the origin. This falls outside the usual range of Landau--Ginzburg theory. Nevertheless Batyrev's procedure provides a way of making sense of these theories.
31 citations
TL;DR: In this paper, the supergravity dual of supersymmetric Yang-Mills theory in 2+1 dimensions with flavor was constructed for fully localized D2/D6 intersection.
Abstract: We construct the supergravity solution for fully localized D2/D6 intersection. The near horizon limit of this solution is the supergravity dual of supersymmetric Yang-Mills theory in 2+1 dimensions with flavor. We use this solution to formulate mirror symmetry of 2+1 dimensional gauge theories in the language of AdS/CFT correspondence. We also construct the supergravity dual of a non-commutative gauge theory with fundamental matter.
31 citations
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TL;DR: In this article, a closed formula for the generating function of genus two Gromov-Witten invariants of quintic 3-folds was derived and the corresponding mirror symmetry conjecture of Bershadsky, Cecotti, Ooguri and Vafa was verified.
Abstract: We derive a closed formula for the generating function of genus two Gromov-Witten invariants of quintic 3-folds and verify the corresponding mirror symmetry conjecture of Bershadsky, Cecotti, Ooguri and Vafa.
31 citations
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TL;DR: In this article, a mirror symmetry of simple elliptic singularities is considered and isomorphisms of Frobenius manifolds among the Gromov-Witten theory of a weighted projective line, the theory of primitive forms for a universal unfolding of a simple singularity and the invariant theory for an elliptic Weyl group are constructed.
Abstract: We consider a mirror symmetry of simple elliptic singularities. In particular, we construct isomorphisms of Frobenius manifolds among the one from the Gromov--Witten theory of a weighted projective line, the one from the theory of primitive forms for a universal unfolding of a simple elliptic singularity and the one from the invariant theory for an elliptic Weyl group. As a consequence, we give a geometric interpretation of the Fourier coefficients of an eta product considered by K. Saito.
31 citations