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Advances in High Energy Physics
Volume 2011, Article ID 357016, 52 pages
Review Article

BPS States, Crystals, and Matrices

1California Institute of Technology, Pasadena, CA 91125, USA
2Faculty of Physics, University of Warsaw, ul. Hoża 69, 00-681 Warsaw, Poland

Received 14 May 2011; Accepted 19 June 2011

Academic Editor: Amihay Hanany

Copyright © 2011 Piotr Sułkowski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We review free fermion, melting crystal, and matrix model representations of wall-crossing phenomena on local, toric Calabi-Yau manifolds. We consider both unrefined and refined BPS counting of closed BPS states involving D2- and D0-branes bound to a D6-brane, as well as open BPS states involving open D2-branes ending on an additional D4-brane. Appropriate limit of these constructions provides, among the others, matrix model representation of refined and unrefined topological string amplitudes.