Marginal Fluctuations as Instantons on M2/D2-Branes

Abstract

We introduce some (anti)M/D-branes through turning on the corresponding field strengths of the eleven- and ten-dimensional supergravity theories over AdS_4 x M^(7/6) spaces, where we use S^7/Z_k and CP^3 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 {\Delta}_+=3. However, after performing a special conformal transformation, we see that the solution is localized in the Euclideanized AdS_4 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 8_s and 8_v for the supercharges and scalars respectively, while the fermions remain fixed in 8_c 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 AdS_5/CFT_4 correspondence. The latter approach covers the difficulty already faced with of the bulk-boundary matching procedure for k=1,2 as well.