  The phase diagram of SU(N) gauge theories with fermions in an arbitrary
representation R can be calculated on finite volume manifolds such as S^1 x
S^3. When S^3 is small a perturbative analysis is possible and the
weak-coupling analogue of the pure Yang-Mills theory confinement-deconfinement
transition is accessible in the large N limit. We calculate the large N phase
diagram of adjoint QCD [SU(N) gauge theory with adjoint fermions] where
periodic boundary conditions are applied to fermions on S^1 such that the
confined phase is favored for light enough adjoint fermion mass. We calculate
the value of the mass times the radius of S^3 below which the confined phase is
favored for all volumes of S^1 / S^3 and discuss the implications for large N
volume reduction. We calculate also the phase diagram for N = 3 and compare
with recent lattice results.
