  Motivated by recent progress on the understanding of the Eguchi-Kawai (EK)
volume equivalence and growing interest in conformal window, we simultaneously
use the large-Nc volume reduction and Chiral Random Matrix Theory (chRMT) to
study the chiral symmetry breaking of four dimensional SU(Nc) gauge theory with
adjoint fermions in the large Nc limit. Although some cares are required
because the chRMT limit and 't Hooft limit are not compatible in general, we
show that the breakdown of the chiral symmetry can be detected in large-Nc
gauge theories. As a first step, we mainly focus on the quenched approximation
to establish the methodology. We first confirm that heavy adjoint fermions,
introduced as the center symmetry preserver, work as expected and thanks to
them the volume reduction holds. Using massless overlap fermion as a probe, we
then calculate the low-lying Dirac spectrum for fermion in the adjoint
representation to compare to that of chRMT, and find that chiral symmetry is
indeed broken in the quenched theory.
