# 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

Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality

- Mathematics
- 2021

For each of the simple Lie algebras g = Al, Dl or E6, we show that the all-genera one-point FJRW invariants of g-type, after multiplication by suitable products of Pochhammer symbols, are the…

## 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…

Intersection theory on M̄1,4 and elliptic Gromov-Witten invariants

- Mathematics
- 1997

We find a new relation among codimension 2 algebraic cycles in the moduli space M1,4, and use this to calculate the elliptic Gromov-Witten invariants of projective spaces CP and CP.…

Intersection theory on the moduli space of curves and the matrix airy function

- Mathematics
- 1992

We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical…

Flat pencils of metrics and Frobenius manifolds

- Mathematics
- 1997

This paper is based on the author's talk at 1997 Taniguchi Symposium ``Integrable Systems and Algebraic Geometry''. We consider an approach to the theory of Frobenius manifolds based on the geometry…