Letters in Mathematical Physics

, Volume 103, Issue 1, pp 59–77 | Cite as

The Remodeling Conjecture and the Faber–Pandharipande Formula

  • Vincent Bouchard
  • Andrei Catuneanu
  • Olivier Marchal
  • Piotr Sułkowski


In this note, we prove that the free energies F g constructed from the Eynard–Orantin topological recursion applied to the curve mirror to \({\mathbb{C}^3}\) reproduce the Faber–Pandharipande formula for genus g Gromov–Witten invariants of \({\mathbb{C}^3}\) . This completes the proof of the remodeling conjecture for \({\mathbb{C}^3}\) .

Mathematics Subject Classification (2010)

14N35 14J33 14J81 


mirror symmetry Gromov–Witten invariants Eynard–Orantin topological recursion remodeling conjecture Hodge integrals matrix models 


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Vincent Bouchard
    • 1
  • Andrei Catuneanu
    • 1
  • Olivier Marchal
    • 1
  • Piotr Sułkowski
    • 2
    • 3
  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.California Institute of TechnologyPasadenaUSA
  3. 3.Faculty of PhysicsUniversity of WarsawWarsawPoland

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