  We study the large-N volume reduction of QCD with adjoint quarks regularized
on the lattice. Specifically, we use Wilson fermions, and while our
d-dimensional lattice has (d-1) infinite dimensions, the remaining direction is
reduced to a point. We perform a weak-coupling one-loop calculation of the free
energy as a function of the holonomy in the reduced direction, and map the
regimes in the bare lattice parameter space where the holonomy averages to zero
and a Z_N-center symmetric configuration is the ground state. For d=4 and
N_f=1/2,1 and 2 Dirac flavors we see that the center symmetry is intact in a
generous regime of the phase diagram that includes the chiral point. Thus we
see that large-N volume independence of lattice QCD with adjoint Wilson quarks
works at weak coupling. Interestingly, we find that this is true even if the
quark mass is quite large, and this opens a path to study the volume reduced
large-N pure gauge theory. Finally, we analyze in detail the UV sensitivity of
the one-loop potential and show that treating the reduced theory as a
(d-1)-dimensional effective field theory requires the introduction of certain
relevant operators that are a subset of those suggested by Unsal and Yaffe to
stabilize the center symmetry. This means that different regularizations of the
volume-reduced theory can be compared only if one includes these terms in the
action.
