Quantum Calabi-Yau and Classical Crystals
arXiv:hep-th/0309208
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 . 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 5-brane web, dual to Calabi-Yau, gets identified with the transition regions of rigid dimer configurations.
26 pages, 8 figures; corrected version
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Cited by in corpus (71)
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