Exact Kahler Potential for Calabi-Yau Fourfolds

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.

40 pages. v2: minor corrections. v3: minor changes, some clarifications in section 4.4 and appendix A.3

References in corpus (5)

• Exact Kahler Potential from Gauge Theory and Mirror Symmetry
• Enumerative geometry of Calabi-Yau 4-folds
• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• The Seiberg-Witten Kahler Potential as a Two-Sphere Partition Function
• Topological Strings on Grassmannian Calabi-Yau manifolds

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