Holomorphic anomaly and matrix models

Details Holomorphic anomaly and matrix models Holomorphic anomaly and matrix models

2007-02-14

arxiv.org/abs/hep-th/0702110v3

JHEP 0706:058,2007

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, LaTex, 3 figures

Scientific paper

10.1088/1126-6708/2007/06/058

The genus g free energies of matrix models can be promoted to modular invariant, non-holomorphic amplitudes which only depend on the geometry of the classical spectral curve. We show that these non-holomorphic amplitudes satisfy the holomorphic anomaly equations of Bershadsky, Cecotti, Ooguri and Vafa. We derive as well holomorphic anomaly equations for the open string sector. These results provide evidence at all genera for the Dijkgraaf--Vafa conjecture relating matrix models to type B topological strings on certain local Calabi--Yau threefolds.

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