Massive (pesudo) scalars in AdS4, SO(4) invariant solutions and holography

Naghdi, M.

doi:10.1140/epjp/i2018-12121-0

Cited by 5 publications

(9 citation statements)

References 60 publications

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“…It is interesting to compare the ansatz with (2.5) in []. As a result, we see that with

U = V = χ = A_{1} = B_{1} = B_{2} = 0

and

f = 6 f_{7}, h = 4 R^{4} {\overset{f}{true}}_{1}, d h = - R^{4} d f_{3},

the formalisms match, and the counterpart of (2.23) in [] is

f = \frac{6}{R^{7}} (ε + h^{2}), ε = \pm {\overset{C}{true}}_{7} R^{6},

which comes from the equation of []. In particular, we read from

*_{4} d false(*_{4} d h false) - false(16 + 24 ε false) h - 2 \times 12 h^{3} = 0,

which is the same as up to some scaling and notice that

R = 1

is set.…”

Section: Special 4‐form Ansatz and Solutionsmentioning

confidence: 98%

“…For the general 4‐form anstaz , we have derived the equations and conditions arising from satisfying the Bianchi identity (

d G_{4} = 0

) and the Euclidean EOM

d *_{11} G_{4} - \frac{i}{2} G_{4} \land G_{4} = 0

in []. However, it is also interesting to discuss the backreaction, that is considering the Einstein's equations as well; and of course we have done it in Appendix , where equations and solutions without and with including the backreaction are analysed in accordance with computations in [] where a more general ansatz is employed.…”

Section: The Background and Genaral Ansatzmentioning

confidence: 99%

“…In particular, we read from

*_{4} d false(*_{4} d h false) - false(16 + 24 ε false) h - 2 \times 12 h^{3} = 0,

which is the same as up to some scaling and notice that

R = 1

is set. Then, from the latter equation, we read

m^{2} R_{A d S}^{2} = - 2

with

ε = - 1

(skew‐whiffed) and

m^{2} R_{A d S}^{2} = 10

with

ε = 1

(Wick‐rotated), which were already discussed in [] and [] respectively.…”

Section: Special 4‐form Ansatz and Solutionsmentioning

confidence: 99%

“…To continue, we note that considering only the EOM means working in probe approximation, that is excluding the backreaction, for which we presented some solutions in [] with dual descriptions. Here we include the backreaction as well.…”

Section: Special 4‐form Ansatz and Solutionsmentioning

confidence: 99%

“…As a result, we found localized or partially localized objects in the bulk of AdS 4 , and explored their boundary CFT 3 holographic duals according to the well‐known AdS/CFT correspondence rules (see [] as an original review). Following the special truncation considered in [] in probe approximation, here we include also the backreaction so that the truncation would be consistent.…”

Section: Introductionmentioning

confidence: 99%

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A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS₄/CFT₃

Naghdi

2018

Fortschritte der Physik

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From a consistent Kaluza-Klein truncation of 11-dimensional supergravity over AdS 4 × C P 3 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) × 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 S O(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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“…It is interesting to compare the ansatz with (2.5) in []. As a result, we see that with

U = V = χ = A_{1} = B_{1} = B_{2} = 0

and

f = 6 f_{7}, h = 4 R^{4} {\overset{f}{true}}_{1}, d h = - R^{4} d f_{3},

the formalisms match, and the counterpart of (2.23) in [] is

f = \frac{6}{R^{7}} (ε + h^{2}), ε = \pm {\overset{C}{true}}_{7} R^{6},

which comes from the equation of []. In particular, we read from

*_{4} d false(*_{4} d h false) - false(16 + 24 ε false) h - 2 \times 12 h^{3} = 0,

which is the same as up to some scaling and notice that

R = 1

is set.…”

Section: Special 4‐form Ansatz and Solutionsmentioning

confidence: 98%

“…For the general 4‐form anstaz , we have derived the equations and conditions arising from satisfying the Bianchi identity (

d G_{4} = 0

) and the Euclidean EOM

d *_{11} G_{4} - \frac{i}{2} G_{4} \land G_{4} = 0

Section: The Background and Genaral Ansatzmentioning

confidence: 99%

“…In particular, we read from

*_{4} d false(*_{4} d h false) - false(16 + 24 ε false) h - 2 \times 12 h^{3} = 0,

which is the same as up to some scaling and notice that

R = 1

is set. Then, from the latter equation, we read

m^{2} R_{A d S}^{2} = - 2

with

ε = - 1

(skew‐whiffed) and

m^{2} R_{A d S}^{2} = 10

with

ε = 1

(Wick‐rotated), which were already discussed in [] and [] respectively.…”

Section: Special 4‐form Ansatz and Solutionsmentioning

confidence: 99%

Section: Special 4‐form Ansatz and Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS₄/CFT₃

Naghdi

2018

Fortschritte der Physik

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Higgs-like (pseudo)scalars in AdS₄, marginal and irrelevant deformations in CFT₃, and instantons on S ³

Naghdi

2024

Chinese Phys. C

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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 $\textbf{8}_s$, $\textbf{8}_c$, $\textbf{8}_v$ 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 $SU(4) \times U(1)$-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. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

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Instantons in AdS$$_4$$ from (anti)membranes wrapping $$S^7$$ to Bose–Fermi duality in CFT$$_3$$’s

Naghdi

2023

Eur. Phys. J. Plus

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Massive (pesudo) scalars in AdS4, SO(4) invariant solutions and holography

Cited by 5 publications

References 60 publications

A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS₄/CFT₃

A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS₄/CFT₃

Higgs-like (pseudo)scalars in AdS₄, marginal and irrelevant deformations in CFT₃, and instantons on S ³

Instantons in AdS$$_4$$ from (anti)membranes wrapping $$S^7$$ to Bose–Fermi duality in CFT$$_3$$’s

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Massive (pesudo) scalars in AdS4, SO(4) invariant solutions and holography

Cited by 5 publications

References 60 publications

A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS4/CFT3

A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS4/CFT3

Higgs-like (pseudo)scalars in AdS4, marginal and irrelevant deformations in CFT3, and instantons on S 3

Instantons in AdS$$_4$$ from (anti)membranes wrapping $$S^7$$ to Bose–Fermi duality in CFT$$_3$$’s

Contact Info

Product

Resources

About

A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS₄/CFT₃

A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS₄/CFT₃

Higgs-like (pseudo)scalars in AdS₄, marginal and irrelevant deformations in CFT₃, and instantons on S ³