  We perform a lattice investigation of QCD with three colors and 2 flavors of
Dirac (staggered) fermions in the adjoint representation, defined on a 4d space
with one spatial dimension compactified, and study the phase structure of the
theory as a function of the size Lc of the compactified dimension. We show that
four different phases take place, corresponding to different realizations of
center symmetry: two center symmetric phases, for large or small values of Lc,
separated by two phases in which center symmetry is broken in two different
ways; the dependence of these results on the quark mass is discussed. We study
also chiral properties and how they are affected by the different realizations
of center symmetry; chiral symmetry, in particular, stays spontaneously broken
at the phase transitions and may be restored at much lower values of the
compactification radius. Our results could be relevant to a recently proposed
conjecture of volume indepedence of QCD with adjoint fermions in the large Nc
limit.
