Crystal melting and black holes

It has recently been shown that the statistical mechanics of crystal meltingmaps 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 threedimensional crystal melting configurations and certain BPS black holes given bybranes wrapping collapsed cycles on the orbifolds C^2/Z_n and C^3/Z_n x Z_n inthe large n limit. The ranks of gauge groups in the associated gauged quiverquantum mechanics determine the profiles of crystal melting configurations andthe process of melting maps to flop transitions which leave the backgroundCalabi-Yau invariant. We explain the connection between these two realizationsof crystal melting and speculate on the underlying physical meaning.Comment: 43 pages, 7 figure