Exact Kahler Potential for Calabi-Yau Fourfolds

TL;DR

This paper investigates the quantum Kahler moduli space of Calabi-Yau fourfolds, proposing an explicit form for the quantum-corrected Kahler potential and validating it through Gromov-Witten invariants and mirror symmetry comparisons.

Contribution

It introduces a conjecture for the quantum Kahler potential of Calabi-Yau fourfolds and computes Gromov-Witten invariants to support this conjecture.

Findings

Proposed an explicit form of the quantum Kahler potential for Calabi-Yau fourfolds.

Computed genus zero Gromov-Witten invariants and validated the conjecture.

Discussed applications to local toric Calabi-Yau varieties.

Abstract

We study quantum Kahler moduli space of Calabi-Yau fourfolds. Our analysis is based on the recent work by Jockers et al. which gives a novel method to compute the Kahler potential on the quantum Kahler moduli space of Calabi-Yau manifold. In contrast to Calabi-Yau threefold, the quantum nature of higher dimensional Calabi-Yau manifold is yet to be fully elucidated. In this paper we focus on the Calabi-Yau fourfold. In particular, we conjecture the explicit form of the quantum-corrected Kahler potential. We also compute the genus zero Gromov-Witten invariants and test our conjecture by comparing the results with predictions from mirror symmetry. Local toric Calabi-Yau varieties are also discussed.