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We perform a lattice investigation of QCD with three colors and 2 flavors ofDirac (staggered) fermions in the adjoint representation, defined on a 4d spacewith one spatial dimension compactified, and study the phase structure of thetheory as a function of the size Lc of the compactified dimension. We show thatfour different phases take place, corresponding to different realizations ofcenter symmetry: two center symmetric phases, for large or small values of Lc,separated by two phases in which center symmetry is broken in two differentways; the dependence of these results on the quark mass is discussed. We studyalso chiral properties and how they are affected by the different realizationsof center symmetry; chiral symmetry, in particular, stays spontaneously brokenat the phase transitions and may be restored at much lower values of thecompactification radius. Our results could be relevant to a recently proposedconjecture of volume indepedence of QCD with adjoint fermions in the large Nclimit.

Finite size phase transitions in QCD with adjoint fermions