Quantum Calabi-Yau and Classical Crystals

TL;DR

This paper introduces a duality linking topological string theory at large coupling to a classical crystal melting model, revealing new insights into Calabi-Yau geometries and statistical mechanics.

Contribution

It proposes a novel duality connecting topological strings with classical crystal melting models and extends this to dimer problems on lattices for toric Calabi-Yau threefolds.

Findings

Recovered topological vertex from crystal melting probabilities

Established duality between string coupling and temperature in crystal models

Connected brane webs with dimer configurations on lattices

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 $g_s$. 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 $(p,q)$ 5-brane web, dual to Calabi-Yau, gets identified with the transition regions of rigid dimer configurations.