Dual Localized Objects From M-Branes Over AdS₄ x S⁷/Z_k

We consider a few ansatzs for the four and seven forms of 11-dimensional supergravity over AdS_4 x S^7/Z_k while try to keep the geometry unchanged. From the 4-form equations, we arrive at some massless scalars and pseudoscalars in the bulk of Euclidean AdS_4 that match with some boundary $\Delta_+$=3 operators. Indeed, the main objects are instantons and domain walls as the fully and partially localized objects in the external space, respectively. The latter comes from an (anti)M5-brane wrapping partly around three internal directions similar to the fuzzy S^3/Z_k solutions. Except for the first solutions of adding some anti-M2-branes$\mid$(M2-branes) to the original M2-branes, the objects backreact on the geometry although small$\mid$(break all supersymmetries and destabilize the vacua). The dual 3-dimensional field theory solutions are got by the skew-whiffing 8_s $\rightarrow$ 8_v and 8_s $\rightarrow$ 8_c for the scalars and pseudoscalars respectively, while the gauge fields are used mainly for the k=1,2 cases where the R-symmetry and supersymmetry are enhanced as SU(4) x U(1) $\rightarrow$ SO(8) and N=6 $\rightarrow$ N=8 respectively, and also for pseudoscalars. Further, for the pseudoscalars we propose a special boundary deformation, with a fermion field, that is equivalent to a multi-trace deformation already studied for the bulk m^2=-2 conformally coupled pseudoscalar.