Consistently melting crystals

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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16 pages, 11 figures

Scientific paper

Recently Ooguri and Yamazaki proposed a statistical model of melting crystals to count BPS bound states of certain D-brane configurations on toric Calabi--Yau manifolds [arXiv:0811.2801]. This construction relied on a set of consistency conditions on the corresponding brane tiling, and in this note I show that these conditions are satisfied for any physical brane tiling; they follow from the conformality of the low energy field theory on the D-branes. As a byproduct I also provide a simple direct proof that any physical brane tiling has a perfect matching.

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