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Emergent Calabi-Yau Geometry · Around

2009

Emergent Calabi-Yau Geometry

Ooguri, Hirosi, Yamazaki, Masahito

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We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper arXiv:0811.2801.

In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the partition function of the topological string theory by relating the Ronkin function of the characteristic polynomial of the crystal melting model to the holomorphic 3-form on the corresponding Calabi-Yau manifold.

Built on

S. K. Donaldson and R. P. Thomas, in The Geometric Universe: Science, Geometry and The Work of Roger Penrose
2000
Earlier work this paper cites.
S. Sheffield, Ph.D. Thesis, Stanford University, 2003
2003
Earlier work this paper cites.
H. Ooguri, A. Strominger and C. Vafa, Phys. Rev. D 70
2004
Earlier work this paper cites.

Similar

L. I. Ronkin, in Complex Analysis in Modern Mathematics (Russian), 239–251, (FAZIS, Moscow, 2001); M. Passare and H. Rullgård, Duke Math. J. 121
2004
Cited alongside, same era.
A. Hanany and K. D. Kennaway, arXiv:hep-th/0503149; S. Franco, A. Hanany, K. D. Kennaway, D. Vegh and B. Wecht, JHEP 0601
2006
Cited alongside, same era.
S. Franco and D. Vegh, JHEP 0611
2006
Cited alongside, same era.
H. Ooguri and M. Yamazaki, Comm. Math. Phys. (to be published), arXiv:0811.2801 [hep-th]
Original
Cited in the paper.
A. Okounkov, N. Reshetikhin and C. Vafa, arXiv:hep-th/0309208
Cited in the paper.
K. Hori and C. Vafa, arXiv:hep-th/0002222
Cited in the paper.
K. Hori, A. Iqbal and C. Vafa, arXiv:hep-th/0005247
Cited in the paper.
S. Mozgovoy and M. Reineke, arXiv:0809.0117 [math.AG]
Original
Cited in the paper.
See, K. Larjo, arXiv:0902.0614 [hep-th], for subsequent developments
Original
Cited in the paper.
R. Kenyon, A. Okounkov and S. Sheffield, arXiv:math-ph/0311005
Cited in the paper.
D. Maulik, A. Oblomkov, A. Okounkov and R. Pandharipande, arXiv:math.AG/0809.3976
Cited in the paper.
M. Kontsevich and Y. Soibelman, arXiv:0811.2435v1 [math.AG]
Original
Cited in the paper.

Then

B. Feng, Y. H. He, K. D. Kennaway and C. Vafa, Adv. Theor. Math. Phys. 12
2008
Later among the works it cites.
B. Szendröi, Geom. Topol. 12
Original
2008
Later among the works it cites.
T. Maeda and T. Nakatsu, Int. J. Mod. Phys. A 22
Original
2008
Later among the works it cites.

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