The planar limit of N=2 superconformal quiver theories

We compute the planar limit of both the free energy and the expectation value of the 1/2 BPS wilson loop for four dimensional N = 2 superconformal quiver theories, with a product of SU(N)s as gauge group and hi-fundamental matter. Supersymmetric localization reduces the problem to a multi-matrix model, that we rewrite in the zero instanton sector as an effective action involving an infinite number of double-trace terms, determined by the relevant extended Cartan matrix. We find that the results, as in the case of N = 2 SCFTs with a simple gauge group, can be written as sums over tree graphs. For the A1<mml:mo stretchy="true"></mml:mover> case, we find that the contribution of each tree can be interpreted as the partition function of a generalized Ising model defined on the tree; we conjecture that the partition functions of these models defined on trees satisfy the Lee-Yang property, i.e. all their zeros lie on the unit circle.