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Author

Eric Zaslow

Other affiliations: Harvard University, Boston College
Bio: Eric Zaslow is an academic researcher from Northwestern University. The author has contributed to research in topics: Mirror symmetry & Fukaya category. The author has an hindex of 31, co-authored 72 publications receiving 6244 citations. Previous affiliations of Eric Zaslow include Harvard University & Boston College.


Papers
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Journal ArticleDOI
TL;DR: In this paper, it was argued that every Calabi-Yau manifold X with a mirror Y admits a family of supersymmetric toroidal 3-cycles and that the moduli space of such cycles together with their flat connections is precisely the space Y.

1,607 citations

Book
01 Jan 2003
TL;DR: In this paper, the authors proved mirror symmetry for supersymmetric sigma models on Calabi-Yau manifolds in 1+1 dimensions and showed that the equivalence of the gauged linear sigma model embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type Standard R -> 1/R duality and dynamical generation of superpotential by vortices.
Abstract: We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type Standard R -> 1/R duality and dynamical generation of superpotential by vortices are crucial in the derivation This provides not only a proof of mirror symmetry in the case of (local and global) Calabi-Yau manifolds, but also for sigma models on manifolds with positive first Chern class, including deformations of the action by holomorphic isometries

1,436 citations

Journal ArticleDOI
TL;DR: In this paper, the authors describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization) using the local geometry near a Fano surface within a Calabi-Yau manifold.
Abstract: We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization). Our results agree with B-model computations from solutions of Picard-Fuchs differential equations constructed form the local geometry near a Fano surface within a Calabi-Yau manifold. We interpret the Gromov-Witten-type numbers from an enumerative point of view. We also describe the geometry of singular surfaces and show how the local invariants of singular surfaces agree with the smooth cases when they occur as complete intersections. † email: chi@math.harvard.edu, yau@math.harvard.edu ∗ email: klemm@ias.edu ∗∗ email: zaslow@math.nwu.edu

329 citations

Journal ArticleDOI
TL;DR: In this article, an isomorphism of categories conjectured by Kontsevich was shown between coherent sheaves on elliptic curves and Lagrangian submanifolds on mirror pairs.
Abstract: We describe an isomorphism of categories conjectured by Kontsevich. If M and f M are mirror pairs then the conjectural equivalence is between the derived category of coherent sheaves on M and a suitable version of Fukaya’s category of Lagrangian submanifolds on f M. We prove this equivalence when M is an elliptic curve and f M is its dual curve, exhibiting the dictionary in detail.

265 citations

Journal ArticleDOI
TL;DR: In this paper, the authors developed a Fukaya $A_\infty$-category for the complex of twisted complexes of Lagrangian branes in the cotangent bundle.
Abstract: Let $X$ be a compact real analytic manifold, and let $T^*X$ be its cotangent bundle. Let $Sh(X)$ be the triangulated dg category of bounded, constructible complexes of sheaves on $X$. In this paper, we develop a Fukaya $A_\infty$-category $Fuk(T^*X)$ whose objects are exact, not necessarily compact Lagrangian branes in the cotangent bundle. We write $Tw Fuk(T^*X)$ for the $A_\infty$-triangulated envelope of $Fuk(T^*X)$ consisting of twisted complexes of Lagrangian branes. Our main result is that $Sh(X)$ quasi-embeds into $Tw Fuk(T^*X)$ as an $A_\infty$-category. Taking cohomology gives an embedding of the corresponding derived categories.

245 citations


Cited by
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20 Jul 1986

2,037 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the Type IIB superstring in ten dimensions has a family of soliton and bound state strings permuted by SL(2, Z ) and the space-time coordinates enter tantalizingly in the formalism as noncommuting matrices.

1,904 citations

Journal ArticleDOI
TL;DR: In this paper, Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves, which is a consequence of an equivalence between the perturbative expansion of = 4 super Yang-Mills theory and the D-instanton expansion of a certain string theory.
Abstract: Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of = 4 super Yang-Mills theory and the D-instanton expansion of a certain string theory, namely the topological B model whose target space is the Calabi-Yau supermanifold

1,626 citations

Posted Content
TL;DR: In this paper, the concept of a generalized Kahler manifold has been introduced, which is equivalent to a bi-Hermitian geometry with torsion first discovered by physicists.
Abstract: Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field. We provide new examples, including some on manifolds admitting no known complex or symplectic structure. We prove a generalized Darboux theorem which yields a local normal form for the geometry. We show that there is an elliptic deformation theory and establish the existence of a Kuranishi moduli space. We then define the concept of a generalized Kahler manifold. We prove that generalized Kahler geometry is equivalent to a bi-Hermitian geometry with torsion first discovered by physicists. We then use this result to solve an outstanding problem in 4-dimensional bi-Hermitian geometry: we prove that there exists a Riemannian metric on the complex projective plane which admits exactly two distinct Hermitian complex structures with equal orientation. Finally, we introduce the concept of generalized complex submanifold, and show that such sub-objects correspond to D-branes in the topological A- and B-models of string theory.

1,380 citations

Journal ArticleDOI
TL;DR: In this paper, a pedagogical overview of flux compactifications in string theory is presented, from the basic ideas to the most recent developments, focusing on closed-string fluxes in type-II theories.

1,085 citations