The holographic contributions to the sphere free energy

We study which bulk couplings contribute to the S³ free energy F(m) of three-dimensional N = 2 superconformal field theories with holographic duals, potentially deformed by boundary real-mass parameters m. In particular, we show that F(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(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, 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(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(m) does not contain information about scaling dimensions or OPE coefficients of single-trace long scalar N = 2 superconformal multiplets.