Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians
TLDR
In this paper, the authors give a mathematical account of a recent string theory calcula- tion which predicts the number of rational curves on the generic quintic three-fold, using the interpretation of Yukawa couplings in terms of variations of Hodge structure, a new q-expansion principle for functions on the moduli space of Calabi-Yau manifolds, and the mirror symmetry.Abstract:
We give a mathematical account of a recent string theory calcula- tion which predicts the number of rational curves on the generic quintic three- fold. Our account involves the interpretation of Yukawa couplings in terms of variations of Hodge structure, a new q-expansion principle for functions on the moduli space of Calabi-Yau manifolds, and the "mirror symmetry" phe- nomenon recently observed by string theorists. DEPARTMENT OF MATHEMATICS, DUKE UNIVERSITY, DURHAM, NORTH CAROLINA 27706 E-mail address: drm@math.duke.edu This content downloaded from 157.55.39.224 on Wed, 14 Dec 2016 04:59:36 UTC All use subject to http://about.jstor.org/termsread more
Citations
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Book ChapterDOI
Homological Algebra of Mirror Symmetry
TL;DR: Mirror symmetry was discovered several years ago in string theory as a duality between families of 3-dimensional Calabi-Yau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeros).
Book ChapterDOI
Geometry of 2D topological field theories
TL;DR: In this paper, the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories is studied, where WDVV equations and Frobenius manifolds are discussed.
Journal Article
Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties
TL;DR: In this article, it was shown that there exists an isomorphism between two conformal field theories corresponding to Calabi-Yau varieties from two families of algebraic compactifications of affine hypersurfaces.
Posted Content
Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
TL;DR: In this article, it was shown that there exists an isomorphism between two conformal field theories corresponding to Calabi-Yau varieties from two families of algebraic compactifications of affine hypersurfaces.
References
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A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
TL;DR: In this paper, the prepotentials and geometry of the moduli spaces for a Calabi-Yau manifold and its mirror were derived and all the sigma model corrections to the Yukawa couplings and moduli space metric were obtained.
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