Quantum Calabi-Yau and classical crystals

Sep, 2003
26 pages
Published in:
  • Prog.Math. 244 (2006) 597
e-Print:
Report number:
  • HUTP-03-A061

Citations per year

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Abstract:
We propose a new duality involving topological strings in the limit of large string coupling constant. The dual is described in terms of a classical statistical mechanical model of crystal melting, where the temperature is inverse of the string coupling constant. The crystal is a discretization of the toric base of the Calabi-Yau with lattice length gsg_s. As a strong evidence for this duality we recover the topological vertex in terms of the statistical mechanical probability distribution for crystal melting. We also propose a more general duality involving the dimer problem on periodic lattices and topological A-model string on arbitrary local toric threefolds. The (p,q)(p,q) 5-brane web, dual to Calabi-Yau, gets identified with the transition regions of rigid dimer configurations.
Note:
  • 26 pages, 8 figures; corrected version
  • string model
  • string: topological
  • space: Calabi-Yau
  • differential forms: Kaehler
  • transfer matrix
  • vertex function
  • partition function
  • duality
  • crystal: classical