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hal-00131013, version 3

Holomorphic anomaly and matrix models

Bertrand Eynard () 1, Marcos Marino () 2, Nicolas Orantin () 1

Abstract: 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.

  • 1:  Service de Physique Théorique (SPhT)
  • CNRS : URA2306 – CEA : DSM/SPHT
  • 2:  European Organization for Nuclear Research (CERN)
  • CERN
  • Domain : Physics/High Energy Physics - Theory
    Physics/Mathematical Physics
    Mathematics/Mathematical Physics
  • Keywords : Holomorphic anomaly – matrix models – modular – string theory – topological expansion
  • Internal note : SPhT-07/020, CERN-PH-TH/2007031
  • Comment : 23 pages – LaTex – 3 figures.
  • Available versions :  v1 (2007-02-14) v2 (2007-03-07) v3 (2007-07-19)
 
  • hal-00131013, version 3
  • http://hal.archives-ouvertes.fr/hal-00131013
  • oai:hal.archives-ouvertes.fr:hal-00131013
  • From: Bertrand Eynard <>
  • Submitted on: Wednesday, 18 July 2007 22:45:48
  • Updated on: Thursday, 19 July 2007 06:45:20