  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.
