  We investigate the quantum forces occurring between the defects and/or
boundaries of a conformal field theory (CFT). We propose to model imperfect
defects and boundaries as localized relevant double-trace operators that deform
the CFT. Our focus is on pointlike and codimension-one planar defects. In the
case of two parallel membranes, we point out that the CFT 2-point function
tends to get confined and develops a tower of resonances with constant decay
rate when the operator dimension approaches the free field dimension. Using a
functional formalism, we compute the quantum forces induced by the CFT between
a variety of configurations of pointlike defects, infinite plates and
membranes. Consistency arguments imply that these quantum forces are attractive
at any distance. Forces of Casimir-Polder type appear in the UV, while forces
of Casimir type appear in the IR, in which case the CFT gets repelled from the
defects. Most of the forces behave as a non-integer power of the separation,
controlled by the dimension of the double-trace deformation. In the Casimir
regime of the membrane-membrane configuration, the quantum pressure behaves
universally as $1/\ell^d$, however information about the double-trace nature of
the defects still remains encoded in the strength of the pressure.
