  We study deformations of three-dimensional large N CFTs by double-trace
operators constructed from spin s single-trace operators of dimension \Delta.
These theories possess UV fixed points, and we calculate the change of the
3-sphere free energy \delta F= F_{UV}- F_{IR}. To describe the UV fixed point
using the dual AdS_4 space we modify the boundary conditions on the spin s
field in the bulk; this approach produces \delta F in agreement with the field
theory calculations. If the spin s operator is a conserved current, then the
fixed point is described by an induced parity invariant conformal spin s gauge
theory. The low spin examples are QED_3 (s=1) and the 3-d induced conformal
gravity (s=2). When the original CFT is that of N conformal complex scalar or
fermion fields, the U(N) singlet sector of the induced 3-d gauge theory is dual
to Vasiliev's theory in AdS_4 with alternate boundary conditions on the spin s
massless gauge field. We test this correspondence by calculating the leading
term in \delta F for large N. We show that the coefficient of (1/2)\log N in
\delta F is equal to the number of spin s-1 gauge parameters that act trivially
on the spin s gauge field. We discuss generalizations of these results to 3-d
gauge theories including Chern-Simons terms and to theories where s is
half-integer. We also argue that the Weyl anomaly a-coefficients of conformal
spin s theories in even dimensions d, such as that of the Weyl-squared gravity
in d=4, can be efficiently calculated using massless spin s fields in AdS_{d+1}
with alternate boundary conditions. Using this method we derive a simple
formula for the Weyl anomaly a-coefficients of the d=4 Fradkin-Tseytlin
conformal higher-spin gauge fields. Similarly, using alternate boundary
conditions in AdS_3 we reproduce the well-known central charge c=-26 of the bc
ghosts in 2-d gravity, as well as its higher-spin generalizations.
