https://doi.org/10.1140/epjc/s10052-014-2826-2
Regular Article - Theoretical Physics
Marginal fluctuations as instantons on M2/D2-branes
Department of Physics, Faculty of Basic Sciences, University of Ilam, Ilam, Iran
* e-mail: m.naghdi@mail.ilam.ac.ir
Received:
16
January
2014
Accepted:
14
March
2014
Published online:
29
March
2014
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.
© SIF and Springer-Verlag Berlin Heidelberg, 2014
