  With a 4-form ansatz of 11-dimensional supergravity over non-dynamical AdS$_4
\times S^7/Z_k$ background, with the internal space as a $S^1$ Hopf fibration
on CP$^3$, we get a consistent truncation. The (pseudo)scalars, in the
resulting scalar equations in Euclidean AdS_4 space, may be viewed as arising
from (anti)M-branes wrapping around internal directions in the (Wick-rotated)
skew-whiffed M2-branes background (as the resulting theory is for
anti-M2-branes) and so, realizing the modes after swapping the three
fundamental representations $8_s, 8_c, 8_v$ of SO(8). Taking the backreaction
on the external and internal spaces, we get massless and massive modes,
corresponding to exactly marginal and marginally irrelevant deformations on the
boundary CFT$_3$, and write a closed solution for the bulk equation and compute
its correction to the background action. Next, considering the Higgs-like
(breathing) mode $m^2=18$, having all supersymmetries, parity and
scale-invariance broken, by solving the associated bulk equation with
mathematical methods, especially the Adomian decomposition method, and
analyzing the behavior near the boundary of the solutions, we realize the
boundary duals in SU(4) x U(1)-singlet sectors of the ABJM model. Then,
introducing new dual deformation $\Delta_+$ = 3, 6 operators made of
bi-fundamental scalars, fermions and U(1) gauge fields, we obtain
SO(4)-invariant solutions as small instantons on a three-sphere with radius at
infinity, which actually correspond to collapsing bulk bubbles leading to
big-crunch singularities.
