Book ChapterDOI
Mirror Symmetry and Elliptic Curves
Robbert Dijkgraaf
- Iss: 129, pp 149-163
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In this article, the authors review how recent results in quantum field theory confirm two general predictions of the mirror symmetry program in the special case of elliptic curves: counting functions of holomorphic curves on a Calabi-Yau space (Gromov-Witten invariants) are quasimodular forms for the mirror family; they can be computed by a summation over trivalent Feynman graphs.Abstract:
I review how recent results in quantum field theory confirm two general predictions of the mirror symmetry program in the special case of elliptic curves: (1) counting functions of holomorphic curves on a Calabi-Yau space (Gromov-Witten invariants) are ‘quasimodular forms’ for the mirror family; (2) they can be computed by a summation over trivalent Feynman graphs.read more
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Journal ArticleDOI
Mirror Principle II
TL;DR: The authors generalize the results in Mirror Principle I to a class of balloon manifolds and extend them to projective manifolds without the convexity assumption, and show that these manifolds can be expressed as convex projective projective models.
Posted Content
Gromov-Witten theory, Hurwitz theory, and completed cycles
TL;DR: In this article, an explicit equivalence between the stationary sector of the Gromov-Witten theory of a target curve X and the enumeration of Hurwitz coverings of X in the basis of completed cycles was established.
Journal ArticleDOI
Topological Strings and (Almost) Modular Forms
TL;DR: The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Γ, generated by monodromies of the periods of X as mentioned in this paper.
Book ChapterDOI
Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions
TL;DR: In this article, the topological string partition function Z(λ,t,t) =exp(λ 2 g-2 Fg(t, t)) is calculated on a compact Calabi-Yau M. Modular properties of the sections Fg as well as local constraints from the 4d effective action allow us to fix Z to a large extent.
Journal Article
Topological Strings And (Almost) Modular Forms
TL;DR: Aganagic et al. as discussed by the authors showed that the genus g topological string amplitude is either a holomorphic quasi-modular form or an almost holomorphic modular form of weight 0 under Γ.
References
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