We introduce some (anti-) M/D-branes through turning on the corresponding field strengths of the 11- and 10-dimensional supergravity theories over spaces, where we use and for the internal spaces. Indeed, when we add M2/D2-branes on the same directions with the near horizon branes of the Aharony-Bergman-Jafferis-Maldacena model, all symmetries and supersymmetries are preserved trivially. In this case, we obtain a localized object just in the horizon. This normalizable bulk massless scalar mode is a singlet of and , and it agrees with a marginal boundary operator of the conformal dimension of . However, after performing a special conformal transformation, we see that the solution is localized in the Euclideanized space and is attributable to the included anti-M2/D2-branes, which are also necessary to ensure that there is no back-reaction. The resultant theory now breaks all supersymmetries to , while the other symmetries are so preserved. The dual boundary operator is then set up from the skew-whiffing of the representations and for the supercharges and scalars, respectively, while the fermions remain fixed in 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 gauge group along the same lines with a similar situation to the one faced in the AdS/CFT correspondence. The latter approach covers the difficulty already faced with in the bulk-boundary matching procedure for as well.
European Physical Journal C
- Pub Date:
- March 2014
- High Energy Physics - Theory
- 21 pages, main structure unchanged, some discussions and references added mainly in the last section, title changed slightly, some typos fixed