  ${\cal N} = 8$ superconformal field theories, such as the ABJM theory at
Chern-Simons level $k=1$ or $2$, contain 35 scalar operators ${\cal O}_{IJ}$
with $\Delta=1$ in the ${\bf 35}_v$ representation of SO(8). The 3-point
correlation function of these operators is non-vanishing, and indeed can be
calculated non-perturbatively in the field theory. But its AdS$_4$ gravity
dual, obtained from gauged ${\cal N}=8$ supergravity, has no cubic $A^3$
couplings in its Lagrangian, where $A^{IJ}$ is the bulk dual of ${\cal
O}_{IJ}$. So conventional Witten diagrams cannot furnish the field theory
result. We show that the extension of bulk supersymmetry to the AdS$_4$
boundary requires the introduction of a finite $A^3$ counterterm that does
provide a perfect match to the 3-point correlator. Boundary supersymmetry also
requires infinite counterterms which agree with the method of holographic
renormalization. The generating functional of correlation functions of the
$\Delta=1$ operators is the Legendre transform of the on-shell action, and the
supersymmetry properties of this functional play a significant role in our
treatment.
