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# 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

#### 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.