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We consider a few ansatzs for the four and seven forms of 11-dimensionalsupergravity 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 pseudoscalarsin the bulk of Euclidean AdS_4 that match with some boundary $\Delta_+$=3operators. Indeed, the main objects are instantons and domain walls as thefully and partially localized objects in the external space, respectively. Thelatter comes from an (anti)M5-brane wrapping partly around three internaldirections similar to the fuzzy S^3/Z_k solutions. Except for the firstsolutions of adding some anti-M2-branes$\mid$(M2-branes) to the originalM2-branes, the objects backreact on the geometry although small$\mid$(break allsupersymmetries and destabilize the vacua). The dual 3-dimensional field theorysolutions are got by the skew-whiffing 8_s $\rightarrow$ 8_v and 8_s$\rightarrow$ 8_c for the scalars and pseudoscalars respectively, while thegauge fields are used mainly for the k=1,2 cases where the R-symmetry andsupersymmetry are enhanced as SU(4) x U(1) $\rightarrow$ SO(8) and N=6$\rightarrow$ N=8 respectively, and also for pseudoscalars. Further, for thepseudoscalars we propose a special boundary deformation, with a fermion field,that is equivalent to a multi-trace deformation already studied for the bulkm^2=-2 conformally coupled pseudoscalar.

Dual Localized Objects From M-Branes Over AdS_4 x S^7/Z_k