Crystal melting and black holes

2006/10/02 by Jonathan J. Heckman, Cumrun Vafa · 25 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Crystal (programming language) #Gauge theory #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Quiver #String (physics) #Theoretical physics #hep-th

paper · pdf · doi:10.1088/1126-6708/2007/09/011

published in Journal of High Energy Physics 2007(09), 011 (Springer Nature) · 43 pages, 7 figures

arxiv created 2006/10/02 · openalex publication_date 2007/09/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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 C²/Z_n and C³/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.

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