Crystal Melting and Black Holes

TL;DR

This paper establishes a correspondence between crystal melting configurations and BPS black holes in certain orbifold backgrounds, linking statistical mechanics, string theory, and black hole physics.

Contribution

It introduces a novel mapping between 3D crystal melting models and BPS black holes via branes on orbifolds, connecting gauge theory profiles to melting processes.

Findings

Mapping between crystal melting and BPS black holes on orbifolds.

Melting processes correspond to flop transitions in Calabi-Yau spaces.

Gauge group ranks determine crystal configurations.

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.