Quiver guage theories, chiral rings and random matrix models

Dimensional deconstruction of 5D SQCD with general nc, nf and kCS gives rise to 4D N = 1 gauge theories with large quivers of SU(nc) gauge factors. We first describe the spectrum of the model in the deconstructive limit and show its properties. We then construct the chiral rings of such theories, off-shell and on-shell. Anomaly equations for the various resolvents allowed by the model permit us to calculate all the relevant chiral operators. The results are broadly similar to the chiral rings of single U(nc) theories with both adjoint and fundamental matter, but there are also some noteworthy differences such as nonlocal meson-like operators where the quark and antiquark fields belong to different nodes of the quiver. And because the analyzed gauge groups are SU(nc) rather than U(nc), our chiral rings also contain a whole collection of baryonic and antibaryonic operators. We then investigate the random matrix model corresponding to such chiral ring. We find that bifundamental chiral operators correspond to unitary matrices. We derive the loop equations and show that they are in perfect agreement with the anomaly equations of the gauge model. An exact expression for the free energy is found in the large Nˆ (rank of the matrix) limit. A formula for the effective superpotential is derived and some examples are illustrated.