Crystal Melting and Black Holes

Abstract

It has recently been shown that the statistical mechanics of crystal melting maps to A-model topological string amplitudes on non-compact Calabi-Yau spaces. In this note we establish a one to one correspondence between two and three dimensional crystal melting configurations and certain BPS black holes given by branes wrapping collapsed cycles on the orbifolds C^2/Z_n and C^3/Z_n x Z_n in the large n limit. The ranks of gauge groups in the associated gauged quiver quantum mechanics determine the profiles of crystal melting configurations and the process of melting maps to flop transitions which leave the background Calabi-Yau invariant. We explain the connection between these two realizations of crystal melting and speculate on the underlying physical meaning.

43 pages, 7 figures

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• Brane Tilings and Their Applications
• Quantum W-symmetry in AdS_3
• Crystal Melting and Toric Calabi-Yau Manifolds
• Wall Crossing, Quivers and Crystals
• Matrix permanent and quantum entanglement of permutation invariant states
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• W(1+infinity) algebra as a symmetry behind AGT relation
• Neurons on Amoebae
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