Quantum Calabi-Yau and classical crystals
Sep, 2003
26 pages
Published in:
- Prog.Math. 244 (2006) 597
e-Print:
- hep-th/0309208 [hep-th]
Report number:
- HUTP-03-A061
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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 . 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.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
References(22)
Figures(9)