Solutions For Scalar Equations in AdS_4 with Adomian Method and Boundary CFT_3 Duals

Abstract: For a nonlinear partial differential equation for (pseudo)scalars in the bulk of Euclidean AdS_4, arising from a truncation of 11-dimensional supergravity over AdS_4 x S^7/Z_k, we use math tools and in particular Adomian Decomposition Method, with initial data from near the boundary behavior of a special or general solution, although we focus on normalizable modes and Dirichlet boundary condition, to get perturbative series solutions (of the equation valid in probe approximation) for three special modes of m^2=4, 0, -9/4. Meantime, we remind that for the skew-whiffed M2-branes background, there are Higgs-like (pseudo)scalars that make the equation homogeneous and provide spontaneous symmetry breaking. Then, with the setups and solutions in the bulk, where all supersymmetries and parity are broken, we swap the three fundamental representations of SO(8) for gravitino, deform the ABJM-like three-dimensional boundary actions with various corresponding SU(4) x U(1)-singlet operators made of fermions, scalars and SU(N) gauge fields, find new SO(4)-invariant instantons, and finally adjust the bulk and boundary solutions and confirm state-operator AdS_4/CFT_3 correspondence.