A Matrix Model for the Topological String I: Deriving the Matrix Model

Bertrand Eynard (1) , Kashani-Poor Amir (1, 2) , Olivier Marchal (3, 1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 IHES - Institut des Hautes Études Scientifiques
3 SPhT - Service de Physique Théorique

We construct a matrix model that reproduces the topological string partition function on arbitrary toric Calabi-Yau threefolds. This demonstrates, in accord with the BKMP "remodeling the B-model" conjecture, that Gromov-Witten invariants of any toric Calabi-Yau threefold can be computed in terms of the spectral invariants of a spectral curve. Moreover, it proves that the generating function of Gromov-Witten invariants is a tau function for an integrable hierarchy. In a follow-up paper, we will explicitly construct the spectral curve of our matrix model and argue that it equals the mirror curve of the toric Calabi-Yau manifold.

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]

Bertrand Eynard, Kashani-Poor Amir, Olivier Marchal. A Matrix Model for the Topological String I: Deriving the Matrix Model. Annales Henri Poincaré, 2014, 15 (10), pp.1867-1901. ⟨10.1007/s00023-013-0290-4⟩. ⟨hal-01062787⟩