Quiver guage theories, chiral rings and random matrix models
Abstract
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.
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