Advances in Theoretical and Mathematical Physics

Volume 13 (2009)

Number 3

On the mathematics and physics of high genus invariants of $[\mathbb{C}^3 / \mathbb{Z}_3]$

Pages: 695 – 719

DOI: http://dx.doi.org/10.4310/ATMP.2009.v13.n3.a4

Authors

Vincent Bouchard (Harvard University)

Renzo Cavalieri (University of Michigan at Ann Arbor)

Abstract

This paper wishes to foster communication between mathematicians and physicists working in mirror symmetry and orbifold Gromov–Witten theory. We provide a reader friendly review of the physics computation in [ABK06] that predicts Gromov–Witten invariants of $[\mathbb{C}^3 / \mathbb{Z}_3]$ in arbitrary genus, and of the mathematical framework for expressing these invariants as Hodge integrals. Using geometric properties of the Hodge classes, we compute the unpointed invariants for $g = 2, 3$, thus providing the first high genus mathematical check of the physics predictions.

Full Text (PDF format)