Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities

Abstract

We construct a two-dimensional crystal melting model which reproduces the BPS index of D2-D0 states bound to a non-compact D4-brane on an arbitrary toric Calabi-Yau singularity. The crystalline structure depends on the toric divisor wrapped by the D4-brane. The molten crystals are in one-to-one correspondence with the torus fixed points of the moduli space of the quiver gauge theory on D-branes. The F- and D-term constraints of the gauge theory are regarded as a generalization of the ADHM constraints on instantons. We also show in several examples that our model is consistent with the wall-crossing formula for the BPS index.

72 pages, 44 figures

References in corpus (17)

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• Amoebas and Instantons
• Statistical model and BPS D4-D2-D0 counting
• Multiple D4-D2-D0 on the Conifold and Wall-crossing with the Flop
• Anomaly Cancellations in Brane Tilings
• Crystals, instantons and quantum toric geometry

Cited by in corpus (16)

• Quiver Yangian from Crystal Melting
• Vafa-Witten invariants from exceptional collections
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{gl}}}_{1|1})$
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• A Note on Quiver Yangians and $\mathcal{R}$-Matrices
• Crystal Melting, BPS Quivers and Plethystics
• Vertical D4-D2-D0 bound states on K3 fibrations and modularity
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• Toric Quiver Asymptotics and Mahler Measure: $\mathcal{N}=2$ BPS States
• Quiver Asymptotics and Amoeba: Instantons on Toric Divisors of Calabi-Yau Threefolds
• Wall-Crossing Effects on Quiver BPS Algebras
• Mock modularity at work, or black holes in a forest
• Mahler Measure for a Quiver Symphony
• Thermodynamics of Isoradial Quivers and Hyperbolic 3-Manifolds
• Weyl Mutations in Quiver Yangians