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The remodeling conjecture and the Faber-Pandharipande formula · Around

2011

The remodeling conjecture and the Faber-Pandharipande formula

Bouchard, Vincent, Catuneanu, Andrei, Marchal, Olivier et al.

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In this note, we prove that the free energies F_g constructed from the Eynard-Orantin topological recursion applied to the curve mirror to C^3 reproduce the Faber-Pandharipande formula for genus g Gromov-Witten invariants of C^3.

This completes the proof of the remodeling conjecture for C^3.

Built on

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C. Faber and R. Pandharipande, “Hodge integrals and Gromov-Witten theory,” Invent. Math. 139
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M. Aganagic, A. Klemm, M. Mariño and C. Vafa, “The Topological Vertex,” Commun. Math. Phys. 254
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C. -C. M. Liu, K. Liu and J. Zhou, “Mariño-Vafa Formula and Hodge Integral Identities,” J. Algebraic Geom. 15
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Similar

B. Eynard and N. Orantin, “Invariants of algebraic curves and topological expansion,” Comm. Numb. Theor. Phys. 1
2007
Cited alongside, same era.
V. Bouchard and M. Mariño, “Hurwitz numbers, matrix models and enumerative geometry,” in From Hodge Theory to Integrability and tQFT: tt*-geometry, Proceedings of Symposia in Pure Mathematics, AMS (2008), arXiv:0709.1458v2 [math.AG]
Original
2008
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B. Eynard, “All orders asymptotic expansion of large partitions,” J. Stat. Mech. P07023 (2008). [arXiv:0804.0381v2 [math-ph]]
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2008
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M. Mariño, “Open string amplitudes and large order behavior in topological string theory,” JHEP 0803
2008
Cited alongside, same era.
V. Bouchard, A. Klemm, M. Mariño and S. Pasquetti, “Remodeling the B-model,” Commun. Math. Phys. 287
Original
2009
Cited alongside, same era.
V. Bouchard and P. Sułkowski, “Topological recursion and mirror curves,” arXiv:1105.2052v1 [hep-th]
Original
Cited in the paper.
L. Chen, “Bouchard-Klemm-Mariño-Pasquetti Conjecture for C**3,” arXiv:0910.3739 [math.AG]
Original
Cited in the paper.
B. Eynard, “Intersection numbers of spectral curves,” arXiv:1104.0176v2 [math-ph]
Original
Cited in the paper.
B. Eynard and C. Kozcaz, “Mirror of the refined topological vertex from a matrix model,” arXiv:1107.5181v1 [hep-th]
Original
Cited in the paper.
B. Eynard, M. Mulase and B. Safnuk, “The Laplace transform of the cut-and-join equation and the Bouchard-Mariño conjecture on Hurwitz numbers,” arXiv:0907.5224v3 [math.AG]
Original
Cited in the paper.
B. Eynard and N. Orantin, “Algebraic methods in random matrices and enumerative geometry,” arXiv:0811.3531v1 [math-ph]
Original
Cited in the paper.
K. Hori and C. Vafa, “Mirror symmetry,” arXiv:hep-th/0002222
Cited in the paper.

Then

B. Eynard, “A matrix model for plane partitions and (T)ASEP,” J. Stat. Mech. 0910
Original
2009
Later among the works it cites.
J. Li, C. -C. M. Liu, K. Liu and J. Zhou, “A Mathematical theory of the topological vertex,” Geom. Topol. 13
2009
Later among the works it cites.
V. Bouchard, A. Klemm, M. Mariño and S. Pasquetti, “Topological open strings on orbifolds,” Commun. Math. Phys. 296
Original
2010
Later among the works it cites.
H. Ooguri, P. Sułkowski, M. Yamazaki, “Wall Crossing As Seen By Matrix Models,” Commun. Math. Phys. (2011) arXiv:1005.1293 [hep-th]
Original
2011
Closest in time.
P. Sułkowski, “Refined matrix models from BPS counting,” Phys. Rev. D83
Original
2011

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