https://doi.org/10.1140/epjp/s13360-023-03905-6
Regular Article
Solutions for scalar equations in AdS
with Adomian method and boundary CFT
duals
1
Department of Physics, Faculty of Basic Sciences, University of Ilam, Ilam, Iran
2
School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran
Received:
13
July
2022
Accepted:
16
March
2023
Published online:
31
March
2023
For a nonlinear partial differential equation for (pseudo)scalars in the bulk of Euclidean AdS4, arising from a truncation of 11-dimensional supergravity over 
, we use math tools and in particular Adomian Decomposition Method, with initial data from near the boundary behavior of a special or general solution, although we focus on normalizable modes and Dirichlet boundary condition, to get perturbative series solutions (of the equation valid in probe approximation) for three special modes of 
. Meantime, we remind that for the skew-whiffed M2-branes background, there are Higgs-like (pseudo)scalars that make the equation homogeneous and provide spontaneous symmetry breaking. Then, with the setups and solutions in the bulk, where all supersymmetries and parity are broken, we swap the three fundamental representations of SO(8) for gravitino, deform the ABJM-like three-dimensional boundary actions with various corresponding 
-singlet operators made of fermions, scalars and SU(N) gauge fields, find new SO(4)-invariant instantons, and finally adjust the bulk and boundary solutions and confirm state-operator AdS/CFT correspondence.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
