Quantum Calabi-Yau and classical crystals

Andrei Okounkov, Nikolai Reshetikhin, Cumrun Vafa

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

144 Citations (Scopus)


We propose a new duality involving topological strings in the limit of the large string coupling constant. The dual is described in terms of a classical statistical mechanical model of crystal melting, where the temperature is the inverse of the string coupling constant. The crystal is a discretization of the toric base of the Calabi-Yau with lattice length g s. As a strong piece of 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) 5-brane web, dual to Calabi-Yau, gets identified with the transition regions of rigid dimer configurations.

Original languageEnglish
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Number of pages22
Publication statusPublished - 2006
Externally publishedYes

Publication series

NameProgress in Mathematics
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X


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