  We study Yang-Mills theory on four dimensional Anti-de Sitter space. The
Dirichlet boundary condition cannot exist at arbitrarily large radius because
it would give rise to colored asymptotic states in flat space. As observed in
[1] this implies a deconfinement-confinement transition as the radius is
increased. We gather hints on the nature of this transition using perturbation
theory. We compute the anomalous dimensions of the lightest scalar operators in
the boundary theory, which are negative for the singlet and positive for
non-trivial representations. We also compute the correction to the coefficient
$C_J$ and we estimate that the singlet operator reaches marginality before the
value of the coupling at which $C_J=0$. These results favor the scenario of
merger and annihilation as the most promising candidate for the transition. For
the Neumann boundary condition, the lightest scalar operator is found to have a
positive anomalous dimension, in agreement with the idea that this boundary
condition extrapolates smoothly to flat space. The perturbative calculations
are made possible by a drastic simplification of the gauge field propagator in
Fried-Yennie gauge. We also derive a general result for the leading-order
anomalous dimension of the displacement operator for a generic perturbation in
Anti-de Sitter, showing that it is related to the beta function of bulk
couplings.
