Emergent Calabi-Yau Geometry

Abstract

We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper arXiv:0811.2801. In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the partition function of the topological string theory by relating the Ronkin function of the characteristic polynomial of the crystal melting model to the holomorphic 3-form on the corresponding Calabi-Yau manifold.

4 pages; v2: revised discussion on wall crossing; v3: typos corrected, published version

References in corpus (7)

• Black Hole Attractors and the Topological String
• Gauge Theories from Toric Geometry and Brane Tilings
• Brane Dimers and Quiver Gauge Theories
• Non-commutative Donaldson-Thomas theory and the conifold
• Moduli Spaces of Gauge Theories from Dimer Models: Proof of the Correspondence
• Intersecting Solitons, Amoeba and Tropical Geometry
• Amoebas and Instantons

Cited by in corpus (31)

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• Open BPS Wall Crossing and M-theory
• Wall Crossing, Quivers and Crystals
• New Integrable Models from the Gauge/YBE Correspondence
• Crystal Melting and Wall Crossing Phenomena
• Wall Crossing As Seen By Matrix Models
• String Theory Origin of Bipartite SCFTs
• Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
• More on topological vertex formalism for 5-brane webs with O5-plane
• BPS State Counting in Local Obstructed Curves from Quiver Theory and Seiberg Duality
• Statistical model and BPS D4-D2-D0 counting
• A note on dimer models and McKay quivers
• Graded Quivers, Generalized Dimer Models and Toric Geometry
• The Non-commutative Topological Vertex and Wall Crossing Phenomena
• The Origin of Calabi-Yau Crystals in BPS States Counting
• A note on statistical model for BPS D4-D2-D0 states
• Crystal Melting, BPS Quivers and Plethystics
• Black hole qubit correspondence from quantum circuits
• Toric Quiver Asymptotics and Mahler Measure: $\mathcal{N}=2$ BPS States
• Quiver Asymptotics and Amoeba: Instantons on Toric Divisors of Calabi-Yau Threefolds
• Decoupling A and B model in open string theory -- Topological adventures in the world of tadpoles
• Mahler Measure for a Quiver Symphony
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• An Overview of Crystals and Double Quiver Yangians
• Thermodynamics of Isoradial Quivers and Hyperbolic 3-Manifolds
• Geometry and Combinatorics of Crystal Melting
• Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux
• Topics in Open Topological Strings