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Domain Wall from Gauged d=4, N=8 Supergravity: Part I
High Energy Physics - Theory · Submitted 3 Sep 2001
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim However, we do have flow equations and domain-wall solutions for the scalar fields are the gradient flow equations of the superpotential that is one of the eigenvalues of A_1 tensor.
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By studying already known extrema of non-semi-simple Inonu-Wigner contraction CSO(p, q)^{+} and non-compact SO(p, q)^{+}(p+q=8) gauged N=8 supergravity in 4-dimensions developed by Hull sometime ago, one expects there exists nontrivial flow in the 3-dimensional boundary field theory. We find that these gaugings provide first-order domain-wall solutions from direct extremization of energy-density. We also consider the most general CSO(p, q, r)^{+} with p+q+r=8 gauging of N=8 supergravity by two successive SL(8,R) transformations of the de Wit-Nicolai theory, that is, compact SO(8) gauged supergravity. The theory found earlier has local SU(8)x CSO(p, q, r)^{+} gauge symmetry as well as local N=8 supersymmetry. The gauge group CSO(p, q, r)^{+} is spontaneously reduced to its maximal compact subgroup SO(p)^{+} x SO(q)^{+} x U(1)^{+r(r-1)/2}. The T-tensor we obtain describes a two-parameter family of gauged N=8 supergravity from which one can construct A_1 and A_2 tensors. The effective nontrivial scalar potential can be written as the difference of positive definite terms. We examine the scalar potential for critical points at which the expectation value of the scalar field is SO(p)^{+} x SO(q)^{+} x SO(r)^{+} invariant. It turns out that there is no new extra critical point. However, we do have flow equations and domain-wall solutions for the scalar fields are the gradient flow equations of the superpotential that is one of the eigenvalues of A_1 tensor.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | By studying already known extrema of non-semi-simple Inonu-Wigner contraction CSO(p, q)^{+} and non-compact SO(p, q)^{+}(p+q=8) gauged N=8 supergravity in 4-dimensions developed by Hull sometime ago, one expects there exists nontrivial flow in the 3-dimensional boundary field theory. | background 0.92 | 0.10 | 0.09 | hedged possibility 0.91 |
| s1 | We find that these gaugings provide first-order domain-wall solutions from direct extremization of energy-density. | result 0.94 | 0.95 | 0.40 | asserted 1.00 |
| s2 | We also consider the most general CSO(p, q, r)^{+} with p+q+r=8 gauging of N=8 supergravity by two successive SL(8,R) transformations of the de Wit-Nicolai theory, that is, compact SO(8) gauged supergravity. | contribution 0.63 | 0.67 | 0.07 | asserted 0.95 |
| s3 | The theory found earlier has local SU(8)x CSO(p, q, r)^{+} gauge symmetry as well as local N=8 supersymmetry. | result 0.64 | 0.36 | 0.06 | asserted 1.00 |
| s4 | The gauge group CSO(p, q, r)^{+} is spontaneously reduced to its maximal compact subgroup SO(p)^{+} x SO(q)^{+} x U(1)^{+r(r-1)/2}. | result 0.97 | 0.52 | 0.10 | asserted 1.00 |
| s5 | The T-tensor we obtain describes a two-parameter family of gauged N=8 supergravity from which one can construct A_1 and A_2 tensors. | result 0.81 | 0.88 | 0.09 | asserted 1.00 |
| s6 | The effective nontrivial scalar potential can be written as the difference of positive definite terms. | result 0.97 | 0.80 | 0.08 | asserted 1.00 |
| s7 | We examine the scalar potential for critical points at which the expectation value of the scalar field is SO(p)^{+} x SO(q)^{+} x SO(r)^{+} invariant. | contribution 0.53 | 0.87 | 0.06 | asserted 0.85 |
| s8 | It turns out that there is no new extra critical point. | result 0.99 | 0.91 | 0.17 | asserted 1.00 |
| s9 | However, we do have flow equations and domain-wall solutions for the scalar fields are the gradient flow equations of the superpotential that is one of the eigenvalues of A_1 tensor. | result 0.91 | 0.92 | 0.43 | asserted 1.00 |
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The paper
Original abstract
By studying already known extrema of non-semi-simple Inonu-Wigner contraction CSO(p, q)^{+} and non-compact SO(p, q)^{+}(p+q=8) gauged N=8 supergravity in 4-dimensions developed by Hull sometime ago, one expects there exists nontrivial flow in the 3-dimensional boundary field theory. We find that these gaugings provide first-order domain-wall solutions from direct extremization of energy-density. We also consider the most general CSO(p, q, r)^{+} with p+q+r=8 gauging of N=8 supergravity by two successive SL(8,R) transformations of the de Wit-Nicolai theory, that is, compact SO(8) gauged supergravity. The theory found earlier has local SU(8)x CSO(p, q, r)^{+} gauge symmetry as well as local N=8 supersymmetry. The gauge group CSO(p, q, r)^{+} is spontaneously reduced to its maximal compact subgroup SO(p)^{+} x SO(q)^{+} x U(1)^{+r(r-1)/2}. The T-tensor we obtain describes a two-parameter family of gauged N=8 supergravity from which one can construct A_1 and A_2 tensors. The effective nontrivial scalar potential can be written as the difference of positive definite terms. We examine the scalar potential for critical points at which the expectation value of the scalar field is SO(p)^{+} x SO(q)^{+} x SO(r)^{+} invariant. It turns out that there is no new extra critical point. However, we do have flow equations and domain-wall solutions for the scalar fields are the gradient flow equations of the superpotential that is one of the eigenvalues of A_1 tensor.
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References
How the literature uses it
14 arXiv papers cite this in 16 sentences
Papers citing it · 11 sentences without a confident label
Uses its method or tool 2 papers
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We use $Γ^1=1_8×8$ and $SO(7)$ gamma matrices $Γ^J$ where $J=2, 3, ⋯, 8$ [ref] .
N=8 Gauged Supergravity Theory and N=6 Superconformal Chern-Simons Matter Theory · The $N=4$ supersymmetric membrane flows in three dimensions · 0.87
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We use $Γ^1=1_8×8$ and $SO(7)$ gamma matrices $Γ^J$ where $J=2, 3, ⋯, 8$ [ref] .
Are There Any New Vacua of Gauged N=8 Supergravity in Four Dimensions? · The $SU(3)$-invariant sector of gauged $N=8$ supergravity with four scalar space · 0.91
Cites it as background 3 papers
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Other domain-walls were explored in refs [ref] for different (electric) gaugings.].
On new maximal supergravity and its BPS domain-walls · Motivation and outlook · 0.88
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As for the study of RG flows, there had been gravity analysis of PW-like flows from early on [ref] .
Klebanov-Witten flows in M-theory · Introduction · 0.99
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For three-dimensional field theories, there are many examples of gravity dual holographic RG flows in gauged $N=8$, $d=4$ supergravity [ref] , and their M-theory uplifts [ref] .
Holographic RG flows on curved manifolds and the $F$-theorem · Conclusions, open questions and outlook · 0.93
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