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Emergent Calabi-Yau geometry.

Hirosi Ooguri1, Masahito Yamazaki

  • 1California Institute of Technology, Pasadena, California 91125, USA.

Physical Review Letters
|June 13, 2009
PubMed
Summary
This summary is machine-generated.

We demonstrate how Calabi-Yau manifold geometry arises from a statistical model of crystal melting. The crystal melting partition function equals the topological string theory partition function in the classical limit.

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Area of Science:

  • Mathematical Physics
  • String Theory
  • Geometry

Background:

  • Calabi-Yau manifolds are crucial in string theory and algebraic geometry.
  • Statistical mechanical models of crystal melting offer a novel approach to studying these manifolds.

Purpose of the Study:

  • To establish a connection between crystal melting models and Calabi-Yau geometry.
  • To demonstrate the emergence of smooth Calabi-Yau geometry from a statistical mechanical framework.

Main Methods:

  • Utilizing the thermodynamic limit of a statistical mechanical model of crystal melting.
  • Relating the Ronkin function of the characteristic polynomial to the holomorphic 3-form.
  • Comparing partition functions from crystal melting and topological string theory.

Main Results:

  • The smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the crystal melting model.
  • The thermodynamic partition function of molten crystals equals the classical limit of the topological string theory partition function.

Conclusions:

  • This work bridges statistical mechanics and string theory, providing new insights into Calabi-Yau geometry.
  • The crystal melting model serves as a powerful tool for understanding topological string theory and related geometric structures.