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arXiv · 0912.0737

Crystal melting on toric surfaces

Michele Cirafici·Amir-Kian Kashani-Poor·Richard J. Szabo
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Abstract

We study the relationship between the statistical mechanics of crystal melting and instanton counting in N=4 supersymmetric U(1) gauge theory on toric surfaces. We argue that, in contrast to their six-dimensional cousins, the two problems are related but not identical. We develop a vertex formalism for the crystal partition function, which calculates a generating function for the dimension 0 and 1 subschemes of the toric surface, and describe the modifications required to obtain the corresponding gauge theory partition function.

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Michele Cirafici, Amir-Kian Kashani-Poor, Richard J. Szabo. 2009-12-04. Crystal melting on toric surfaces. https://doi.org/10.1016/j.geomphys.2011.06.014

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