Dimer Models and Integrable Systems

Understand

We explore various aspects of the correspondence between dimer models and integrable systems recently introduced by Goncharov and Kenyon.

• Dimer models give rise to relativistic integrable systems that match those arising from 5d N=1 gauge theories studied by Nekrasov.
• We apply the correspondence to dimer models associated to the Y^{p,0} geometries, showing that they give rise to the relativistic generalization of the periodic Toda chain originally studied by Ruijsenaars.
• The correspondence reduces the calculation of all conserved charges to a straightforward combinatorial problem of enumerating non-intersecting paths in the dimer model.