On Emergent Geometry of the Gromov-Witten Theory of Quintic Calabi-Yau Threefold
@article{Zhou2020OnEG, title={On Emergent Geometry of the Gromov-Witten Theory of Quintic Calabi-Yau Threefold}, author={Jian Zhou}, journal={arXiv: Mathematical Physics}, year={2020} }
We carry out the explicit computations that are used to write down the integrable hierarchy associated with the quintic Calabi-Yau threefold. We also do the calculations for the geometric structures emerging in the Gromov-Witten theory of the quintic, such as the Frobenius manifold structure and the special K\"ahler structure.
One Citation
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References
SHOWING 1-10 OF 47 REFERENCES
Gromov - Witten invariants and integrable hierarchies of topological type
- Mathematics
- 2013
We outline two approaches to the construction of integrable hierarchies associated with the theory of Gromov - Witten invariants of smooth projective varieties. We argue that a comparison of these…
Quantum Cohomology at Higher Genus: Topological Recursion Relations and Virasoro Conditions
- Mathematics
- 1998
We construct topological recursion relations (TRR’s) at higher genera g ≥ 2 for general 2-dimensional topological field theories coupled to gravity. These TRR’s when combined with Virasoro conditions…
Topological Recursions of Eynard–Orantin Type for Intersection Numbers on Moduli Spaces of Curves
- Mathematics
- 2013
We prove that the Virasoro constraints satisfied by the higher Weil–Petersson volumes of moduli spaces of curves are equivalent to Eynard–Orantin topological recursions for some spectral curve. This…
ON ALMOST DUALITY FOR FROBENIUS MANIFOLDS
- Mathematics
- 2003
We present a universal construction of almost duality for Frobenius man- ifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We…
On Itzykson-Zuber Ansatz
- PhysicsJournal of High Energy Physics
- 2019
Abstract
We apply the renormalized coupling constants and Virasoro constraints to derive the Itzykson-Zuber Ansatz on the form of the free energy in 2D topological gravity. We also treat the 1D…
Topological recursion relations in genus 2
- Mathematics
- 1998
In Part 1 of this paper, we study gravitational descendents of Gromov-Witten invariants for general projective manifolds, applying the Behrend-Fantechi construction of the virtual fundamental…
Hodge integrals and Gromov-Witten theory
- Mathematics
- 1998
Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these…
Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
- Mathematics
- 2001
We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov - Witten invariants of all genera into the…