Marginal Fluctuations as Instantons on M2/D2-Branes

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We introduce some (anti)M/D-branes through turning on the corresponding field strengths of the eleven- and ten-dimensional supergravity theories over AdS₄ x M(7/6) spaces, where we use S⁷/Zₖ and CP³ for the internal spaces. Indeed, when we add M2/D2-branes on the same directions with the near horizon branes of Aharony-Bergman-Jafferis-Maldacena model, all symmetries and supersymmetries are preserved trivially. In the case, we gain a localized object just in the horizon. This normalizable bulk massless scalar mode is a singlet of SO(8) and SU(4)x U(1), and agrees with a marginal boundary operator of the conformal dimension of Δ+=3. However, after performing a special conformal transformation, we see that the solution is localized in the Euclideanized AdS₄ space and is attributable to the included anti-M2/D2-branes, which are also necessary to ensure that there is no backreaction. The resultant theory now breaks all N=8,6 supersymmetries to N=0 while other symmetries are so preserved. The dual boundary operator then sets up from the skew-whiffing of the representations 8ₛ and 8ᵥ for the supercharges and scalars respectively, while the fermions remain fixed in 8c of the original theory. Besides, we also address another alternate bulk to boundary matching procedure through turning on one of the gauge fields of the full U(N)ₖ x U(N)-k gauge group in the same lines with the similar situation faced in AdS₅/CFT₄ correspondence. The latter approach covers the difficulty already faced with of the bulk-boundary matching procedure for k=1,2 as well.