  We study which bulk couplings contribute to the $S^3$ free energy
$F(\mathfrak{m})$ of three-dimensional ${\cal N} = 2$ superconformal field
theories with holographic duals, potentially deformed by boundary real-mass
parameters $\mathfrak{m}$. In particular, we show that $F(\mathfrak{m})$ is
independent of a large class of bulk couplings that include non-chiral F-terms
and all D-terms. On the other hand, in general, $F(\mathfrak{m})$ does depend
non-trivially on bulk chiral F-terms, such as prepotential interactions, and on
bulk real-mass terms. These conclusions can be reached solely from properties
of the AdS super-algebra, $\mathfrak{osp}(2|4)$. We also consider massive
vector multiplets in AdS, which in the dual field theory correspond to long
single-trace superconformal multiplets of spin zero. We provide evidence that
$F(\mathfrak{m})$ is insensitive to the vector multiplet mass and to the
interaction couplings between the massive vector multiplet and massless ones.
In particular, this implies that $F(\mathfrak{m})$ does not contain information
about scaling dimensions or OPE coefficients of single-trace long scalar ${\cal
N} = 2$ superconformal multiplets.
