arXiv subjects

M. Naghdi

Publications and source records attributed to M. Naghdi.

13 recordsLinked to original sources

arXiv2023

Higgs-like (pseudo)Scalars in AdS$_4$, Marginal and Irrelevant Deformations in CFT_3 and Instantons on S^3

With a 4-form ansatz of 11-dimensional supergravity over non-dynamical AdS$_4 \times S^7/Z_k$ background, with the internal space as a $S^1$ Hopf fibration on CP$^3$, we get a consistent truncation. The (pseudo)scalars, in the resulting scalar equations in Euclidean AdS_4 space, may be viewed as arising from (anti)M-branes wrapping around internal directions in the (Wick-rotated) skew-whiffed M2-branes background (as the resulting theory is for anti-M2-branes) and so, realizing the modes after swapping the three fundamental representations $8_s, 8_c, 8_v$ of SO(8). Taking the backreaction on the external and internal spaces, we get massless and massive modes, corresponding to exactly marginal and marginally irrelevant deformations on the boundary CFT$_3$, and write a closed solution for the bulk equation and compute its correction to the background action. Next, considering the Higgs-like (breathing) mode $m^2=18$, having all supersymmetries, parity and scale-invariance broken, by solving the associated bulk equation with mathematical methods, especially the Adomian decomposition method, and analyzing the behavior near the boundary of the solutions, we realize the boundary duals in SU(4) x U(1)-singlet sectors of the ABJM model. Then, introducing new dual deformation $\Delta_+$ = 3, 6 operators made of bi-fundamental scalars, fermions and U(1) gauge fields, we obtain SO(4)-invariant solutions as small instantons on a three-sphere with radius at infinity, which actually correspond to collapsing bulk bubbles leading to big-crunch singularities.

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arXiv2023

Instantons in AdS$_4$ From (anti)Membranes Wrapping $S^7$ To Bose-Fermi Duality in CFT$_3$'s

We present new SO(4)-invariant and non-supersymmetric instanton solutions for the conformally coupled m^2=-2 and massive m^2=+4 (pseudo)scalars arising from a consistent truncation of 11-dimensional supergravity over AdS_4 x S^7/Z_k when the internal space is a S^1 Hopf fibration on CP^3, and we consider backreaction. In fact, the bulk configurations associate with (anti)membranes wrapped around mixed internal (and external) directions, which in turn probe the Wick-rotated or skew-whiffed background, break all supersymmetries as well as parity invariance. From near the boundary behavior of the closed solution for the coupled bulk (pseudo)scalar, we get a marginal triple-trace deformation with mixed boundary condition (valid also for the bulk massless m^2=0 (pseudo)scalar, raised when considering the external space backreaction, with Dirichlet boundary condition) and as a result, the corresponding boundary effective potential is unbounded from below and causes an instability because of the Fubini-like instanton. Presenting dual effective actions, we see that the boundary solutions and counterparts realize in singlet sectors of three-dimensional U(N) and O(N) Chern--Simons-matter field theories. In particular, we use versions of massless and mass-deformed regular and critical boson and fermion models, find instantons and confirm state-operator AdS_4/CFT_3 correspondence and also Bose-Fermi duality at the level of the solutions. In addition, we discuss on relations of our setups with Vasiliev's Higher-Spin theories, deformations of the Aharony-Bergman-Jafferis-Maldacena model and other related studies.

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arXiv2020

Solutions For Scalar Equations in AdS_4 with Adomian Method and Boundary CFT_3 Duals

For a nonlinear partial differential equation for (pseudo)scalars in the bulk of Euclidean AdS_4, arising from a truncation of 11-dimensional supergravity over AdS_4 x S^7/Z_k, 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 m^2=4, 0, -9/4. 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 SU(4) x U(1)-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_4/CFT_3 correspondence.

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arXiv2018

A Truncation of 11-Dimensional Supergravity for Fubini-Like Instantons in AdS_4/CFT_3

From a consistent Kaluza-Klein truncation of 11-dimensional supergravity over AdS_4 x CP^3 x S^1/Z_k, with a general 4-form ansatz, we arrive at a set of equations and solutions for the included fields. In particular, we have a bulk equation for a self-interacting (pseudo)scalar with arbitrary mass. By computing the energy-momentum tensors of the associated Einstein equations, to include the backreaction, and setting them to zero, we solve the resulting equations with the bulk one and get solutions corresponding to marginal and marginally relevant deformations of the boundary CFT_3, which break the conformal symmetry. These bulk (pseudo)scalars are SU(4) x U(1)-singlet and the corresponding solutions break all supersymmetries and parity because of the associated (anti)M-branes wrapping around specific and mixed internal and external directions. As a result and according to AdS_4/CFT_3 duality rules, we would realize the boundary counterpart in three-dimensional Chern-Simon U(N) field theories with matters in fundamental representations. In particular, we build a SO(4)-invariant Fubini-like instanton solution by setting a specific boundary Lagrangian. The resulting solution is used to describe the dynamics of thin-wall bubbles that cause instability and big crunch singularities in the bulk because of the unboundedness of the boundary double-hump potential from below. Relations to mass-deformed ABJM model, O(N) vector models and scale invariance breaking are also discussed. Meanwhile, we evaluate corrections for the background actions because of the bulk and boundary instantons.

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arXiv2017

Massive (pesudo)Scalars in AdS$_4$, SO(4) Invariant Solutions and Holography

We include a new 7-form ansatz in 11-dimensional supergravity over AdS_4 x S^7/Z_k when the internal space is considered as a U(1) bundle on CP^3. After a general analysis of the ansatz, we take a special form of it and obtain a scalar equation from which we focus on a few massive bulk modes that are SU(4) x U(1) R-singlet and break all supersymmetries. The mass term breaks the scale invariance and so the (perturbative) solutions we obtain are SO(4) invariant in Euclidean AdS_4 (or SO(3,1) in its dS_3 slicing). The corresponding bare operators are irrelevant in probe approximation; and to realize the AdS_4/CFT_3 correspondence, we need to swap the fundamental representations of $SO(8)$ for supercharges with those for scalars and fermions. In fact, we have domain-walls arising from (anti)M5-branes wrapping around S^3/Z_k of the internal space with parity breaking scheme. As a result, the duals may be in three-dimensional U(N) or O(N) Chern-Simon models with matters in fundamental representations. Accordingly, we present dual boundary operators and build instanton solutions in a truncated version of the boundary ABJM action; and, because of the unboundedness of bulk potential from below, it is thought that they lead to big crunch singularities in the bulk.

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arXiv2016

Non-Minimally Coupled Pseudoscalars in AdS_4 for Instantons in CFT_3

For the 11-dimensional supergravity over AdS_4 x S^7/Z_k, beginning with a general 4-from ansatz and the main geometry unchanged, we get a tower of massive and tachyonic pseudoscalars. Indeed, the resultant equations can be assigned to the so-called $ϕ^4$ actions of the non-minimally coupled scalar-tensor theories with a cosmological constant. We focus on a well-known tachyonic and a new massive bulk mode, which are singlet under the internal group and break all supersymmetries, associated with skew-whiffing and Wick-rotating of the background 4-from flux, respectively. The first one is the conformally coupled m^2=-2 pseudoscalar in the bulk of Euclidean AdS_4, where an exact instanton solution is found and a marginally triple-trace deformation with a proper dimension-1 operator produces an agreeing boundary solution with finite action. From the action evaluated on the solution, we estimate the decay rate of the vacuum tunneling mediated by the instanton. Another massive m^2=+4 mode, with the so-called non-minimal coupling parameter $ξ= - 1/3$, also breaks the conformal invariance and so, there is no exact solution. Then, based on the AdS_4/CFT_3 correspondence rules, we propose the dimension-4 ($Δ_+ = +4$) boundary operator in the skew-whiffed (anti-M2-branes) theory to deform the boundary action- consisting of a singlet fermion, an original scalar and U(1) gauges fields- with and find some solutions to be matched with the bulk solutions.

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arXiv2015

Dual Localized Objects From M-Branes Over AdS_4 x S^7/Z_k

We consider a few ansatzs for the four and seven forms of 11-dimensional supergravity over AdS_4 x S^7/Z_k while try to keep the geometry unchanged. From the 4-form equations, we arrive at some massless scalars and pseudoscalars in the bulk of Euclidean AdS_4 that match with some boundary $Δ_+$=3 operators. Indeed, the main objects are instantons and domain walls as the fully and partially localized objects in the external space, respectively. The latter comes from an (anti)M5-brane wrapping partly around three internal directions similar to the fuzzy S^3/Z_k solutions. Except for the first solutions of adding some anti-M2-branes$\mid$(M2-branes) to the original M2-branes, the objects backreact on the geometry although small$\mid$(break all supersymmetries and destabilize the vacua). The dual 3-dimensional field theory solutions are got by the skew-whiffing 8_s $\rightarrow$ 8_v and 8_s $\rightarrow$ 8_c for the scalars and pseudoscalars respectively, while the gauge fields are used mainly for the k=1,2 cases where the R-symmetry and supersymmetry are enhanced as SU(4) x U(1) $\rightarrow$ SO(8) and N=6 $\rightarrow$ N=8 respectively, and also for pseudoscalars. Further, for the pseudoscalars we propose a special boundary deformation, with a fermion field, that is equivalent to a multi-trace deformation already studied for the bulk m^2=-2 conformally coupled pseudoscalar.

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arXiv2014

Nucleon-Nucleon Interaction: A Typical/Concise Review

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.

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arXiv2013

Comparing Some Nucleon-Nucleon Potentials

The aim is to compare a few Nucleon-Nucleon (NN) potentials especially Reid68, Reid68-Day, Reid93, UrbanaV14, ArgonneV18, Nijmegen 93, Nijmegen I and Nijmegen II. Although these potentials have some likenesses and are almost phenomenological, they include in general different structures and their own characteristics. The potentials are constructed in a manner that fit the NN scattering data or phase shifts and are compared in this way. A high-quality scale of a potential is that it fits the data with $χ^{2}/N_{data} \approx 1$, describes well the deuteron properties and gives satisfactory results in nuclear-structure calculations. However, these scales have some failures. Here, we first compare many potentials by confronting them with the data. Then, we try to compare the potential forms by considering the potential structures directly and therefore regarding their substantial bases somehow. To do so, we note that since the potentials are written in different schemas, it is necessary to write them in a unique schema. On the other hand, because three major terms in the NN interaction are central, tensor and spin-orbit terms; so, to perform a reduction plan and arrive at a common structure, we choose the Reid's potential form. Next, we compare the potentials for some states and address some other related issues as well.

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arXiv2013

Marginal Fluctuations as Instantons on M2/D2-Branes

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 Δ_+=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.

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arXiv2013

New Instantons in AdS_4/CFT_3 from D4-Branes Wrapping Some of CP^3

With use of a 6-form field strength of ten-dimensional type IIA supergravity over AdS_4 x 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)x 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 Δ=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.

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arXiv2011

A Monopole Instanton-Like Effect in the ABJM Model

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.

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arXiv2011

Dual Instantons in Anti-membranes Theory

We introduce two ansatzs for the 3-form potential of Euclidean 11d supergravity on skew-whiffed AdS_4 X S^7 background which results in two scalar modes with m^2=-2 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 SU(4) subgroup of SO(8) isometry group, whereas there are no corresponding SU(4) singlet BPS operators of dimensions one or two on the boundary ABJM theory. Noticing the interchange of 8_s and 8_c representations under skew-whiffing in the bulk, we propose the theory of anti-membranes should similarly be obtained from ABJM 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.

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