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
Hilbert schemes, integrable hierarchies, and Gromov-Witten theory
TL;DR: In this paper, a correspondence between the equivariant intersection on Hilbert schemes and stationary Gromov-Witten theory is established, which is a result of the use of 2-Toda hierarchies.
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Double Hurwitz numbers via the infinite wedge
Paul Johnson,Paul Johnson +1 more
TL;DR: In this paper, the authors derive explicit formulas for certain generating functions of double Hurwitz numbers, which generalize a formula in the work of Goulden, Jackson, and Vakil.
Book
Topological Strings and Quantum Curves
TL;DR: In this paper, the duality between Vafa-Witten theory and WZW models is embedded in string theory, with a central role for Riemann surfaces, and a geometric analysis of wall-crossing in N=4 string theory is presented.
Journal ArticleDOI
Counting Feynman-like graphs: Quasimodularity and Siegel-Veech weight
Elise Goujard,Martin Möller +1 more
TL;DR: In this paper, the quasimodularity of generating functions for counting torus covers with and without Siegel-Veech weight was shown to arise as contour integral of quasi-elliptic functions.
References
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