  Superconformal indices of 3d N=2 supersymmetric field theories are
investigated from the Yang-Baxter equation point of view. Solutions of the
star-triangle relation, vertex and IRF Yang-Baxter equations are expressed in
terms of the q-special functions associated with these 3d indices. For a
two-dimensional monopole-spin system on the square lattice a free energy per
spin is explicitly determined. Similar to the partition functions,
superconformal indices of 3d theories with the chiral symmetry breaking reduce
to Dirac delta functions with the support on chemical potentials of the
preserved flavor groups.
