Quantum Calabi-Yau and Classical Crystals View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2007

AUTHORS

Andrei Okounkov , Nikolai Reshetikhin , Cumrun Vafa

ABSTRACT

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. More... »

PAGES

597-618

References to SciGraph publications

  • 1998-01-06. Webs of (p,q) 5-branes, five dimensional field theories and grid diagrams in JOURNAL OF HIGH ENERGY PHYSICS
  • 2005-03. The Topological Vertex in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1994-10. Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2001-08. The Low-Temperature Expansion of the Wulff Crystal in the 3D Ising Model in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Book

    TITLE

    The Unity of Mathematics

    ISBN

    978-0-8176-4076-7

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/0-8176-4467-9_16

    DOI

    http://dx.doi.org/10.1007/0-8176-4467-9_16

    DIMENSIONS

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