We introduce two ansatzs for the 3-form potential of Euclidean 11d supergravity on skew-whiffed AdS 4 Â S 7 background which results in two scalar modes with m 2 ¼ À2 on AdS 4 . Being conformally coupled with a quartic interaction, it is possible to find the exact solutions of the scalar equation on this background. These modes turn out to be invariant under the SUð4Þ subgroup of the SOð8Þ isometry group, whereas there are no corresponding SUð4Þ singlet Bogomol'nyi-Prasad-Sommerfeld operators of dimensions one or two on the boundary theory constructed by Aharony, Bergman, Jafferis, and Maldacena. Noticing the interchange of 8 s and 8 c representations under skew-whiffing in the bulk, we propose the theory of antimembranes should similarly be obtained from Aharony, Bergman, Jafferis, and Maldacena's theory by swapping these representations. In particular, this enables us to identify the dual boundary operators of the two scalar modes. We deform the boundary theory by the dual operators and examine the fermionic field equations, and compare the solutions of the deformed theory with those of the bulk.
With use of a 6-form field strength of ten-dimensional type IIA supergravity over AdS 4 × CP 3 , when S 7 /Z k is considered as a S 1 Hopf fibration on CP 3 , we earn a fully localized solution in the bulk of Euclideanized AdS 4 . Indeed, this object appears in the external space because of wrapping a D4(M5)-brane over some parts of the respective internal spaces. Interestingly, this supersymmetry breaking SU(4) × U(1)-singlet mode exists in already known spectra when one uses the 8 c gravitino representation of SO(8). To adjust the boundary theory, we should swap the original 8 s and 8 c representations for supercharges and fermions in the Aharony-Bergman-Jafferis-Maldacena model. The procedure could later be interpreted as adding an anti-D4(M5)-brane to the prime N = 6 membrane theory resulting in a N = 0 antimembrane theory while other symmetries are preserved. Then, according to the well-known state-operator correspondence rules, we find a proper dual operator with the conformal dimension of ∆ + = 3 that matches to the bulk massless pseudoscalar state. After that, by making use of some fitting ansatzs for the used matter fields, we arrive at an exact boundary solution and comment on the other related issues as well. * E-Mail: m.naghdi@mail.ilam.ac.ir
Nearly a recent century of work is divided to Nucleon-Nucleon (NN) interaction issue. We review some overall perspectives of NN interaction with a brief discussion about deuteron, general structure and symmetries of NN Lagrangian as well as equations of motion and solutions. Meanwhile, the main NN interaction models, as frameworks to build NN potentials, are reviewed concisely. We try to include and study almost all well-known potentials in a similar way, discuss more on various commonly used plain forms for two-nucleon interaction with an emphasis on the phenomenological and meson-exchange potentials as well as the constituent-quark potentials and new ones based on chiral effective field theory and working in coordinate-space mostly. The potentials are constructed in a way that fit NN scattering data, phase shifts, and are also compared in this way usually. An extra goal of this study is to start comparing various potentials forms in a unified manner. So, we also comment on the advantages and disadvantages of the models and potentials partly with reference to some relevant works and probable future studies. * E-Mail: m.naghdi@mail.ilam.ac.ir
Making use of ansatzs for the form fields in the 10d type IIA supergravity version of the ABJM model, we come with a solution in the Euclidean signature recognized as a monopole instanton-like object. Indeed we will see that we can have a (anti) self-dual solution at a special limit. While as a topological object, its back-reaction on the original background should be ignorable, we show the energy-momentum tensors vanish exactly. On the field theory side, the best counterpart is an U(1) gauge field of a gauge transformation. To adjust with bulk, the gauge field must prompt to a dynamic one without adding any kinetic term for this dual photon except a marginal, abelian AB-type Chern-Simons term on the boundary. We will see how both side solutions match next to another confirmation from some earlier works of this vortex-particle duality.
We introduce some (anti-) M/D-branes through turning on the corresponding field strengths of the 11-and 10-dimensional supergravity theories over AdS 4 × M 7|6 spaces, where we use S 7 /Z k and C P 3 for the internal spaces. Indeed, when we add M2/D2-branes on the same directions with the near horizon branes of the Aharony-Bergman-JafferisMaldacena 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 SO (8) and SU (4) × U (1), and it agrees with a marginal boundary operator of the conformal dimension of + = 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 back-reaction. The resultant theory now breaks all N = 8, 6 supersymmetries to N = 0, while the other symmetries are so preserved. The dual boundary operator is then set 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 × U (N ) −k gauge group along the same lines with a similar situation to the one faced in the AdS 5 /CFT 4 correspondence. The latter approach covers the difficulty already faced with in the bulk-boundary matching procedure for k = 1, 2 as well.
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