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New N=2 Supersymmetric Membrane Flow In Eleven-Dimensional Supergravity
High Energy Physics - Theory · Submitted 21 Sep 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim With an appropriate 3-form gauge field, we find an exact solution to the 11-dimensional Einstein-Maxwell equations corresponding to the above lift of the SU(2) x U(1) x U(1)_R-invariant RG flow.
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The abstract, sentence by sentence
We construct the 11-dimensional lift of the known N=2 supersymmetric RG flow solution in 4-dimensional N=8 gauged supergravity. The squashed and stretched 7-dimensional internal metric preserving SU(2) x U(1) x U(1)_R symmetry contains an Einstein-Kahler 2-fold which is a base manifold of 5-dimensional Sasaki-Einstein Y^{p, q} space found in 2004. The nontrivial r(transverse to the domain wall)-dependence of the AdS_4 supergravity fields makes the Einstein-Maxwell equations consistent not only at the critical points but also along the supersymmetric whole RG flow connecting two critical points. With an appropriate 3-form gauge field, we find an exact solution to the 11-dimensional Einstein-Maxwell equations corresponding to the above lift of the SU(2) x U(1) x U(1)_R-invariant RG flow. The particular limits of this solution give rise to the previous solutions with SU(3) x U(1)_R or SU(2) x SU(2) x U(1)_R.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We construct the 11-dimensional lift of the known N=2 supersymmetric RG flow solution in 4-dimensional N=8 gauged supergravity. | contribution 1.00 | 0.95 | 0.29 | asserted 1.00 |
| s1 | The squashed and stretched 7-dimensional internal metric preserving SU(2) x U(1) x U(1)_R symmetry contains an Einstein-Kahler 2-fold which is a base manifold of 5-dimensional Sasaki-Einstein Y^{p, q} space found in 2004. | result 0.52 | 0.56 | 0.09 | asserted 1.00 |
| s2 | The nontrivial r(transverse to the domain wall)-dependence of the AdS_4 supergravity fields makes the Einstein-Maxwell equations consistent not only at the critical points but also along the supersymmetric whole RG flow connecting two critical points. | result 0.83 | 0.75 | 0.26 | asserted 0.99 |
| s3 | With an appropriate 3-form gauge field, we find an exact solution to the 11-dimensional Einstein-Maxwell equations corresponding to the above lift of the SU(2) x U(1) x U(1)_R-invariant RG flow. | result 0.76 | 0.97 | 0.58 | asserted 1.00 |
| s4 | The particular limits of this solution give rise to the previous solutions with SU(3) x U(1)_R or SU(2) x SU(2) x U(1)_R. | result 0.85 | 0.80 | 0.14 | asserted 1.00 |
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The paper
Original abstract
We construct the 11-dimensional lift of the known N=2 supersymmetric RG flow solution in 4-dimensional N=8 gauged supergravity. The squashed and stretched 7-dimensional internal metric preserving SU(2) x U(1) x U(1)_R symmetry contains an Einstein-Kahler 2-fold which is a base manifold of 5-dimensional Sasaki-Einstein Y^{p, q} space found in 2004. The nontrivial r(transverse to the domain wall)-dependence of the AdS_4 supergravity fields makes the Einstein-Maxwell equations consistent not only at the critical points but also along the supersymmetric whole RG flow connecting two critical points. With an appropriate 3-form gauge field, we find an exact solution to the 11-dimensional Einstein-Maxwell equations corresponding to the above lift of the SU(2) x U(1) x U(1)_R-invariant RG flow. The particular limits of this solution give rise to the previous solutions with SU(3) x U(1)_R or SU(2) x SU(2) x U(1)_R.
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How the literature uses it
3 arXiv papers cite this in 29 sentences
Papers citing it · 17 sentences without a confident label
Compares with it 2 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 for $SU(3) ×U(1)_R$ symmetry case [ref] , $SU(2) ×SU(2) ×U(1)_R$, or $SU(2) ×U(1) ×U(1)_R$ [ref] exactly.
The Eleven-Dimensional Uplift of Four-Dimensional Supersymmetric RG Flow · An $N=2$ supersymmetric flow in an 11-dimensional theory · 0.91
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The three coordinates [ref] are related to those in this paper: $(μ, α)$ correspond to $(þ, þ_6)$ of ([ref]) and $ψ=þ_5$.
Holographic N=1 Supersymmetric Membrane Flows · An $N=1$ $SU(2) ×U(1)$-invariant supersymmetric flow · 0.87
Cites it as background 3 papers
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The 11-dimensional description preserving $N=2$ $SU(2) ×U(1) ×U(1)_R$ symmetry is found in [ref] and the smaller $N=2$ $U(1) ×U(1) ×U(1)_R$ symmetry flow is discussed in [ref] .
Holographic N=1 Supersymmetric Membrane Flows · Introduction · 0.84
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Recently, the 11-dimensional description preserving $SU(2) ×U(1) ×U(1)_R$ symmetry is found in [ref] .
The Eleven-Dimensional Uplift of Four-Dimensional Supersymmetric RG Flow · Introduction · 0.87
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The 11-dimensional description preserving $N=2$ $SU(2) ×U(1) ×U(1)_R$ symmetry is found in [ref] and the smaller $N=2$ $U(1) ×U(1) ×U(1)_R$ symmetry flow is discussed in [ref] .
Towards An N=1 SU(3)-Invariant Supersymmetric Membrane Flow In Eleven-Dimensional Supergravity · Introduction · 0.89
What it cites · 31 sentences without a confident label
Builds on 2 papers
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At first, let us replace the 4-dimensional $CP^1 ×CP^1$ space appearing in the 7-dimensional internal space in [ref] with the 4-dimensional Einstein-Kahler 2-fold which lives in the five-dimensional $Y^p,q$ space [ref] .
An N = 2 Supersymmetric Membrane Flow · An $N=2$ supersymmetric $SU(2) ×U(1) ×U(1)_R$-invariant flow in an 11-dimensional theory · 0.98
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At first, let us replace the 4-dimensional $CP^1 ×CP^1$ space appearing in the 7-dimensional internal space in [ref] with the 4-dimensional Einstein-Kahler 2-fold which lives in the five-dimensional $Y^p,q$ space [ref] .
Sasaki-Einstein Metrics on S^2 x S^3 · An $N=2$ supersymmetric $SU(2) ×U(1) ×U(1)_R$-invariant flow in an 11-dimensional theory · 0.98
Uses the method or tool of 1 paper
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The main procedure given in [ref] is to start with the round compactification in terms of $U(1)$-fibration over the Einstein-Kahler 3-fold, to squash this Einstein-Kahler base ellipsoidally, to stretch the $U(1)$ fiber, and to introduce 3-form tensor gauge potential proportional to the volume form on the base.
An N = 2 Supersymmetric Membrane Flow · Introduction · 0.84
Compares with 2 papers
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Note that the one-form in subsection 4.1 of [ref] is the $U(1)$ bundle over the 4-dimensional $CP^2$ space while the one-form in Eq. (4.38) of [ref] is the $U(1)$ bundle over the 4-dimensional $CP^1 ×CP^1$ space.
An N = 2 Supersymmetric Membrane Flow · An $N=2$ supersymmetric $SU(2) ×U(1) ×U(1)_R$-invariant flow in an 11-dimensional theory · 0.83
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This nontrivial boundary conditions also occur for the $N=1$ $G_2$ M2-brane flow in 11-dimensions [ref] .
An N=1 Supersymmetric G_2-invariant Flow in M-theory · The 4-form field strength in frame basis · 0.98
Cites as background 13 papers
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The holographic supersymmetric RG flow equation connecting $N=8$ $SO(8)$ point to $N=2$ $SU(3) ×U(1)$ point has been studied in [ref] where the $U(1)$ symmetry here can be identified with $U(1)_R$ symmetry of 3-dimensional theory coming from the $N=2$ supersymmetry while those from $N=8$ $SO(8)$ point to $N=1$ $G_2$ point has been studied in [ref] .
Three-Dimensional SCFTs, Supersymmetric Domain Wall and Renormalization Group Flow · Introduction · 0.89
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The holographic supersymmetric RG flow equation connecting $N=8$ $SO(8)$ point to $N=2$ $SU(3) ×U(1)$ point has been studied in [ref] where the $U(1)$ symmetry here can be identified with $U(1)_R$ symmetry of 3-dimensional theory coming from the $N=2$ supersymmetry while those from $N=8$ $SO(8)$ point to $N=1$ $G_2$ point has been studied in [ref] .
An N=1 Supersymmetric G_2-invariant Flow in M-theory · Introduction · 0.89
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The holographic supersymmetric RG flow equation connecting $N=8$ $SO(8)$ point to $N=2$ $SU(3) ×U(1)$ point has been studied in [ref] where the $U(1)$ symmetry here can be identified with $U(1)_R$ symmetry of 3-dimensional theory coming from the $N=2$ supersymmetry while those from $N=8$ $SO(8)$ point to $N=1$ $G_2$ point has been studied in [ref] .
Supersymmetric Domain Wall and RG Flow from 4-Dimensional Gauged N=8 Supergravity · Introduction · 0.89
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