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The Gauge Dual of A Warped Product of AdS_4 and A Squashed and Stretched Seven-Manifold
High Energy Physics - Theory · Submitted 18 Aug 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We identify the gauge dual of this background with the theory described by Franco, Klebanov and Rodriguez-Gomez recently.
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The abstract, sentence by sentence
Corrado, Pilch and Warner in 2001 have found the second 11-dimensional solution where the deformed geometry of S^7 in the lift contains S^2 x S^2. We identify the gauge dual of this background with the theory described by Franco, Klebanov and Rodriguez-Gomez recently. It is the U(N) x U(N) x U(N) gauge theory with two SU(2) doublet chiral fields B_1 transforming in the (N, Nbar, 1), B_2 transforming in the (1, N, Nbar), C_1 in the (1, Nbar, N) and C_2 in the (Nbar, N, 1) as well as an adjoint field \Phi in the (1, adj, 1) representation. By adding the mass term for adjoint field \Phi, the detailed correspondence between fields of AdS_4 supergravity and composite operators of the IR field theory is determined. Moreover, we compute the spin-2 KK modes around a warped product of AdS_4 and a squashed and stretched seven-manifold. This background with global SU(2) x SU(2) x U(1)_R symmetry is related to a U(N) x U(N) x U(N) N=2 superconformal Chern-Simons matter theory with eighth-order superpotential and Chern-Simons level (1,1,-2). The mass-squared in AdS_4 depends on SU(2) x SU(2) x U(1)_R quantum numbers and KK excitation number. The dimensions of spin-2 operators are found.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Corrado, Pilch and Warner in 2001 have found the second 11-dimensional solution where the deformed geometry of S^7 in the lift contains S^2 x S^2. | background 1.00 | 0.02 | 0.06 | asserted 1.00 |
| s1 | We identify the gauge dual of this background with the theory described by Franco, Klebanov and Rodriguez-Gomez recently. | result 0.50 | 0.91 | 0.47 | asserted 1.00 |
| s2 | It is the U(N) x U(N) x U(N) gauge theory with two SU(2) doublet chiral fields B_1 transforming in the (N, Nbar, 1), B_2 transforming in the (1, N, Nbar), C_1 in the (1, Nbar, N) and C_2 in the (Nbar, N, 1) as well as an adjoint field \Phi in the (1, adj, 1) representation. | result 0.55 | 0.48 | 0.24 | asserted 1.00 |
| s3 | By adding the mass term for adjoint field \Phi, the detailed correspondence between fields of AdS_4 supergravity and composite operators of the IR field theory is determined. | method 0.46 | 0.86 | 0.13 | asserted 1.00 |
| s4 | Moreover, we compute the spin-2 KK modes around a warped product of AdS_4 and a squashed and stretched seven-manifold. | contribution 0.91 | 0.94 | 0.12 | asserted 1.00 |
| s5 | This background with global SU(2) x SU(2) x U(1)_R symmetry is related to a U(N) x U(N) x U(N) N=2 superconformal Chern-Simons matter theory with eighth-order superpotential and Chern-Simons level (1,1,-2). | result 0.80 | 0.60 | 0.33 | asserted 1.00 |
| s6 | The mass-squared in AdS_4 depends on SU(2) x SU(2) x U(1)_R quantum numbers and KK excitation number. | result 0.99 | 0.80 | 0.08 | asserted 1.00 |
| s7 | The dimensions of spin-2 operators are found. | result 0.98 | 0.90 | 0.16 | asserted 1.00 |
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The paper
Original abstract
Corrado, Pilch and Warner in 2001 have found the second 11-dimensional solution where the deformed geometry of S^7 in the lift contains S^2 x S^2. We identify the gauge dual of this background with the theory described by Franco, Klebanov and Rodriguez-Gomez recently. It is the U(N) x U(N) x U(N) gauge theory with two SU(2) doublet chiral fields B_1 transforming in the (N, Nbar, 1), B_2 transforming in the (1, N, Nbar), C_1 in the (1, Nbar, N) and C_2 in the (Nbar, N, 1) as well as an adjoint field \Phi in the (1, adj, 1) representation. By adding the mass term for adjoint field \Phi, the detailed correspondence between fields of AdS_4 supergravity and composite operators of the IR field theory is determined. Moreover, we compute the spin-2 KK modes around a warped product of AdS_4 and a squashed and stretched seven-manifold. This background with global SU(2) x SU(2) x U(1)_R symmetry is related to a U(N) x U(N) x U(N) N=2 superconformal Chern-Simons matter theory with eighth-order superpotential and Chern-Simons level (1,1,-2). The mass-squared in AdS_4 depends on SU(2) x SU(2) x U(1)_R quantum numbers and KK excitation number. The dimensions of spin-2 operators are found.
Human review
References
How the literature uses it
9 arXiv papers cite this in 23 sentences
Papers citing it · 15 sentences without a confident label
Uses its method or tool 1 paper
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Similar to the cases studied in [ref] , applying the separation of variables to the transverse and traceless (with respect to the $AdS_4$ metric $g_4μν$ without the warp factor) part of $ĥ_μν$, ĥ_μν=h_μν(x)Y(y), ∇_4^μh_μν=0, g_4^μνh_μν=0, we find that the spin-2 modes solving the homogenous linearized Einstein equation satisfy Y(y)L^-2_0(_4+2)h_μν+h_μνOY(y)=0, L^2_0=3√(3) /16,
Evidence for the Holographic dual of ${\cal N}=3$ Solution in Massive Type IIA · Kaluza-Klein spectrum of Spin-2 fluctuations · 0.96
Compares with it 1 paper
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It turns out the Ricci tensor is identical to the one with $SU(3) ×U(1)_R$ symmetry [ref] , the one with $SU(2) ×SU(2) ×U(1)_R$ symmetry [ref] or the one with $SU(2) ×U(1) ×U(1)_R$ symmetry [ref] .
The Eleven-Dimensional Uplift of Four-Dimensional Supersymmetric RG Flow · An $N=2$ supersymmetric flow in an 11-dimensional theory · 0.99
Cites it as background 5 papers
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The gauge dual with the symmetry of $SU(2) ×SU(2) ×U(1)_R$ for the 11-dimensional lift of $SU(3) ×U(1)_R$-invariant solution in 4-dimensional supergravity is described in [ref] .
The Eleven-Dimensional Uplift of Four-Dimensional Supersymmetric RG Flow · Introduction · 0.93
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These lead to new proposals of $AdS_4/CFT_3$ [ref] , in which the dynamics of the IR CFTs are still governed by certain superconformal Chern-Simons matter theories with more than one gauge groups.
Evidence for the Holographic dual of ${\cal N}=3$ Solution in Massive Type IIA · Introduction · 0.92
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The gauge dual with $N=2$ $SU(2) ×SU(2) ×U(1)_R$ symmetry for the 11-dimensional lift of $SU(3) ×U(1)_R$-invariant solution in 4-dimensional supergravity is described in [ref] (see also [ref] ).
Holographic N=1 Supersymmetric Membrane Flows · Introduction · 0.86
What it cites · 73 sentences without a confident label
Contests 1 paper
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in order to describe the 4-form $F^(4)$ that solves ([ref]) in the frame basis together with ([ref]) [ Let us emphasize that the form of ([ref]) is different from the one in [ref] where maybe the careless typing was done. 1) The imaginary $i$ should be in the exponent of exponential function and 2) the coefficient in $e^10$ should be changed in the original paper [ref] .].
An N = 2 Supersymmetric Membrane Flow · An $N=2$ supersymmetric $SU(2) ×SU(2) ×U(1)_R$-invariant flow in an 11-dimensional theory · contest 0.88
Uses the method or tool of 5 papers
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In section 3, the $OSp(2|4)$ representations and $SU(2) ×SU(2) ×U(1)_R$ representations in the supergravity mass spectrum for each multiplet at the $N=2$ critical point and the corresponding $N=2$ superfields in the dual gauge theory are given in the spirit of [ref] .
Holographic Supergravity Dual to Three Dimensional N=2 Gauge Theory · Introduction · 0.84
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In section 3, the $OSp(2|4)$ representations and $SU(2) ×SU(2) ×U(1)_R$ representations in the supergravity mass spectrum for each multiplet at the $N=2$ critical point and the corresponding $N=2$ superfields in the dual gauge theory are given in the spirit of [ref] .
Towards Holographic Gravity Dual of N=1Superconformal Chern-Simons Gauge Theory · Introduction · 0.84
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In section 4, the minimally coupled scalar equation [ref] in the background of section 2 and the mass formula are determined.
The Squashed, Stretched, and Warped Gets Perturbed · Introduction · 0.95
Uses data or values from 2 papers
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At the UV end of the flow which is just $AdS_4 ×S^7$, $A(r) ∼2/L r$ from the solution for $A(r)$ and $W=1$ [ref] .
Three-Dimensional SCFTs, Supersymmetric Domain Wall and Renormalization Group Flow · $OSp(2|4)$ spectrum and operator map between bulk and boundary theories · 0.84
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where the corresponding $(m_1, m_2)$ values are $(1,1), (0,1)$ and $(-1,-1)$ respectively [ref] .
Gauge/Gravity Duality and Warped Resolved Conifold · KK spectrum of minimally coupled scalar · 0.89
Compares with 3 papers
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After substituting ([ref]) into the right hand side of Einstein equation ([ref]) with frame basis ([ref]) one reproduces the one of $SU(3) ×U(1)_R$ case [ref] exactly.
The Squashed, Stretched, and Warped Gets Perturbed · The 4-form field strength and the Ricci tensor in frame basis for $SU(2) ×SU(2) ×U(1)_R$-invariant case · 0.90
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After substituting ([ref]) into the right hand side of Einstein equation ([ref]) with frame basis ([ref]) one reproduces the one of $SU(3) ×U(1)_R$ case [ref] exactly.
An N = 2 Supersymmetric Membrane Flow · The 4-form field strength and the Ricci tensor in frame basis for $SU(2) ×SU(2) ×U(1)_R$-invariant case · 0.90
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The matter contents and the superpotential of this theory are the same as for the D3-branes on the conifold [ref] .
Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity · Introduction · 0.80
Cites as background 17 papers
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In section 2, the 11-dimensional background [ref] is reviewed.
An N = 2 Supersymmetric Membrane Flow · Introduction · 0.95
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The mass deformed $U(2) ×U(2)$ Chern-Simons matter theory with level $k=1, 2$ preserving global $SU(3) ×U(1)_R$ symmetry has been studied in [ref] by identifying the turning on the supergravity fields with the mass term in the boundary gauge theory while the mass deformation for this theory preserving $G_2$ symmetry has been described in [ref] .
The Squashed, Stretched, and Warped Gets Perturbed · Introduction · 0.81
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The mass deformed $U(2) ×U(2)$ Chern-Simons matter theory with level $k=1, 2$ preserving global $SU(3) ×U(1)_R$ symmetry has been studied in [ref] by identifying the turning on the supergravity fields with the mass term in the boundary gauge theory while the mass deformation for this theory preserving $G_2$ symmetry has been described in [ref] .
Holographic Supergravity Dual to Three Dimensional N=2 Gauge Theory · Introduction · 0.81
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