On Emergent Geometry of the Gromov-Witten Theory of Quintic Calabi-Yau Threefold

TL;DR

This paper explicitly computes the integrable hierarchy and geometric structures like Frobenius and special K"ahler structures in the Gromov-Witten theory of the quintic Calabi-Yau threefold, advancing understanding of its mathematical properties.

Contribution

It provides detailed calculations of the integrable hierarchy and geometric structures associated with the Gromov-Witten theory of the quintic Calabi-Yau threefold, which were previously not explicitly known.

Findings

Explicit integrable hierarchy for the quintic Calabi-Yau threefold

Detailed descriptions of Frobenius manifold structures

Insights into the special K"ahler geometry in Gromov-Witten theory

Abstract

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.