The fluctuating seven-sphere in eleven-dimensional supergravity

Biran, Bernard; Casher, A.; Englert, François; Rooman, Marianne; Spindel, Philippe

doi:10.1016/0370-2693(84)90666-x

Cited by 127 publications

(154 citation statements)

References 9 publications

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“…The spectrum of KK harmonics and linearized equations of motion around the type IIA string background can then easily be derived from the AdS 4 results [17] upon a further dimensional reduction. We focus on bosonic fluctuations.…”

Section: Linearized Equation Of Motions Via Reduction From Adsmentioning

confidence: 99%

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Supergravity Duals of Matrix String Theory

Morales¹,

Samtleben²

2002

J. High Energy Phys.

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We study holographic duals of type II and heterotic matrix string theories described by warped AdS 3 supergravities. By explicitly solving the linearized equations of motion around near horizon D-string geometries, we determine the spectrum of Kaluza-Klein primaries for type I, II supergravities on warped AdS 3 × S 7 . The results match those coming from the dual two-dimensional gauge theories living on the D-string worldvolumes. We briefly discuss the connections with the N = (8, 8), N = (8, 0) orbifold superconformal field theories to which type IIB/heterotic matrix strings flow in the infrared. In particular, we associate the dimension (h,h) = ( 3 2 , 3 2 ) twisted operator which brings the matrix string theories out from the conformal point (R 8 ) N /S N with the dilaton profile in the supergravity background.The familiar dictionary between masses and "scaling" dimensions of field and operators are modified by the presence of non-trivial warp factors and running dilatons. These modifications are worked out for the general case of domain wall/QFT correspondences between supergravities on warped AdS d+1 × S q geometries and super Yang-Mills theories with 16 supercharges.

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Section: Linearized Equation Of Motions Via Reduction From Adsmentioning

confidence: 99%

“…The spectrum of masses λ has been derived in [17]. It is organized in supermultiplets of the group OSp(8|4, R).…”

Section: Linearized Equation Of Motions Via Reduction From Adsmentioning

confidence: 99%

Supergravity Duals of Matrix String Theory

Morales¹,

Samtleben²

2002

J. High Energy Phys.

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“…This follows easily from the known mass formula [16] M 2 = ∆ L − 4m 2 , where the Lichnerowicz operator ∆ L has eigenvalues ∆ L = [n(n + 6) + 12]m 2 for O +(2) , and the fact that M 2 is traditionally defined according to (∆ AdS − 8m 2 + M 2 )S = 0. For 300 (corresponding to n = 2), M 2 300 = 16m 2 and this ought to equal to Eq.…”

Section: So(8) Invariant Conformal Fixed Pointmentioning

confidence: 89%

Three-dimensional CFTs and RG flow from squashing M2-brane horizon

Ahn

Rey

2000

Nuclear Physics B

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Utilizing AdS/CFT correspondence in M-theory, an example of interacting d = 3 conformal field theories and renormalization group flow between them is presented. Near-horizon geometry of N coincident M2-branes located on a conical singularity on eight-dimensional hyperkähler manifold or manifold with Spin(7) holonomy is, in large-N limit, AdS 4 × X 7 , where X 7 is seven-sphere with squashing. Deformation from round S 7 to squashed one is known to lead to spontaneous breaking of N = 8 local supersymmetry in gauged AdS 4 supergravity to N = 1, 0. Via AdS/CFT correspondence, it is interpreted as renormalization group flow from SO(5)×SO(3) symmetric UV fixed point to SO(8) symmetric IR fixed point. Evidences for the interpretation are found both from supergravity scalar potential and existence of interpolating static domain-wall thereof, and from conformal dimensions of relevant chiral primary operator at each fixed point.

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“…3 In this section we apply the KK reduction to the 11-dimensional gravity on AdS 4 × S 7 to obtain 4-dimensional equation of motion on AdS 4 background. Such KK reduction was carried out in the de Donder gauge in [30,31]. However, the LLM solutions of our interest in this paper are in a different gauge and can not be analyzed based on the results obtained in the de Donder gauge.…”

Section: Kk Reduction and Gauge Invariant Modesmentioning

confidence: 99%

Mass-deformed ABJM theory and LLM geometries: exact holography

Jang

Kim

Kwon

et al. 2017

J. High Energ. Phys.

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We present a detailed account and extension of our claim in arXiv:1610.01490. We test the gauge/gravity duality between the N = 6 mass-deformed ABJM theory with U k (N )×U −k (N ) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(4)/Z k ×SO(4)/Z k isometry, in the large N limit. Our analysis is based on the evaluation of vacuum expectation values of chiral primary operators from the supersymmetric vacua of mass-deformed ABJM theory and from the implementation of Kaluza-Klein holography to the LLM geometries. We focus on the chiral primary operator with conformal dimension ∆ = 1. We show that O (∆=1) = N 3 2 f (∆=1) for all supersymmetric vacuum solutions and LLM geometries with k = 1, where the factor f (∆) is independent of N . We also confirm that the vacuum expectation value of the energy momentum tensor is vanishing as expected by the supersymmetry. We extend our results to the case of k = 1 for LLM geometries represented by rectangular-shaped Young-diagrams. In analogy with the Coulomb branch of the N = 4 super Yang-Mills theory, we argue that the discrete Higgs vacua of the mABJM theory as well as the corresponding LLM geometries are parametrized by the vevs of the chiral primary operators.

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The fluctuating seven-sphere in eleven-dimensional supergravity

Cited by 127 publications

References 9 publications

Supergravity Duals of Matrix String Theory

Supergravity Duals of Matrix String Theory

Three-dimensional CFTs and RG flow from squashing M2-brane horizon

Mass-deformed ABJM theory and LLM geometries: exact holography

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