Integrable Structure of $5d$ $\mathcal{N}=1$ Supersymmetric Yang-Mills and Melting Crystal

We study loop operators of $5d$ $\mathcal{N}=1$ SYM in $\Omega$ background. For the case of U(1) theory, the generating function of correlation functions of the loop operators reproduces the partition function of melting crystal model with external potential. We argue the common integrable structure of $5d$ $\mathcal{N}=1$ SYM and melting crystal model.
Comment: 12 pages, 1 figure, based on an invited talk presented at the international workshop "Progress of String Theory and Quantum Field Theory" (Osaka City University, December 7-10, 2007), to be published in the proceedings