  A general class of holographic theories with a nontrivial $\theta$-angle are
analyzed. The instanton density operator is dual to a bulk axion field. We
calculate the ground-state solutions with nontrivial source, $a_{UV}$, for the
axion, for both steep and soft dilaton potentials in the IR, and both in $d=3$
and $d=4$. We find all cases to be qualitatively similar. We also calculate the
spin$=2,0$ glueball spectra and show that the glueball masses monotonically
decrease as functions of $a_{UV}$ (or $\theta$-angle). The slopes of glueball
masses are different, generically, in different potentials. In the case of
steep dilaton potentials, the glueball (masses)$^2$ turn negative before the
maximum of $a_{UV}$ is attained. We interpret this as a signal for a favored
instanton condensation in the bulk. We also investigate strong CP-violation in
the effective glueball action.
