Emergent Calabi-Yau Geometry
High Energy Physics - Theory
2009-05-13 v3 Algebraic Geometry
Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0902.3996,
title = {Emergent Calabi-Yau Geometry},
author = {Hirosi Ooguri and Masahito Yamazaki},
journal= {arXiv preprint arXiv:0902.3996},
year = {2009}
}
Comments
4 pages; v2: revised discussion on wall crossing; v3: typos corrected, published version