Crystal melting on toric surfaces

Details Crystal melting on toric surfaces Crystal melting on toric surfaces

2009-12-04

arxiv.org/abs/0912.0737v2

Physics

High Energy Physics

High Energy Physics - Theory

30 pages; v2: references added

Scientific paper

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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