TY - CHAP

T1 - Quantum Calabi-Yau and classical crystals

AU - Okounkov, Andrei

AU - Reshetikhin, Nikolai

AU - Vafa, Cumrun

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84930353028&partnerID=8YFLogxK

U2 - 10.1007/0-8176-4467-9_16

DO - 10.1007/0-8176-4467-9_16

M3 - Chapter

AN - SCOPUS:84930353028

T3 - Progress in Mathematics

SP - 597

EP - 618

BT - Progress in Mathematics

PB - Springer Basel

ER -