Supersymmetric AdS_5 solutions of M-theory

Daniel Waldram; Dario Martelli; James Sparks; Jerome P. Gauntlett

REVIEW

Supersymmetric AdS_5 solutions of M-theory

Jerome P. Gauntlett, Dario Martelli, James Sparks, Daniel Waldram

High Energy Physics - Theory · Submitted 19 Feb 2004 · 48 references

Pith's verdict: The local classification in (2.52)–(2.58) is the real contribution and it holds up; the explicit-solution half is solid where worked out, but §5.3's S²×S² non-KE branch is asserted rather than demonstrated, and the abstract states the base classification unconditionally.

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arXiv IDhep-th/0402153 (version 2)

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CitationDaniel Waldram, Dario Martelli, James Sparks, Jerome P. Gauntlett. "Supersymmetric AdS_5 solutions of M-theory." arXiv:hep-th/0402153 (2004). https://pith.science/paper/WHN5OV4O

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Editor's note

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The thing worth your time here is section 2, not the solution zoo. Gauntlett, Martelli, Sparks and Waldram take the D=11 Killing spinor equation, decompose the spinor into bilinears, and show that any warped AdS5×M6 background with four-form flux is locally fixed by a one-parameter family of four-dimensional Kähler metrics with a y-independent complex structure, plus a single angular function ζ. The derivation is careful and, importantly, cross-checked: section 2.2 reproduces the same conditions from the independent d=7 SU(3) analysis of Kaste–Minasian–Tomasiello, and the Bianchi identity and G equation of motion are shown to follow from supersymmetry rather than imposed separately. That is a real result and it is the reason people cite this paper. Appendix D is also worth a look — they claim Minkowski5 vacua with flux exist, contra the Behrndt–Gukov superpotential argument, and the resolution (that argument assumed Calabi–Yau) is clean and checkable. The §4.1 KE family is worked properly: the conical-singularity coefficient α²=1 is checked at both poles, and the c<4 regularity statement is earned. §5.1's c=0 metric (5.8) is explicit and its regularity is visible by inspection. Where I'd push back is §5.3. The abstract says the base is 'either (i) KE with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces', full stop. But §5.3, which is where the non-Einstein S²×S² and S²×H² cases with a1≠a2 live, only says 'for various ranges of (a1,a2,c) there are regular solutions' and that existence 'is rather easy to see if one sets c=0'. No ranges, no positivity check, no pole analysis. That's the one place the abstract outruns the text. It's a fixable gap, not a wrong claim, and the Goldberg caveat in §3.2 is properly flagged by the authors — I wouldn't hold that against them. Who should read it: anyone working on flux compactifications or G-structure classifications, and anyone who wants the local geometry behind the Sasaki–Einstein family in the companion paper. Send it to referees; the section 2 derivation deserves scrutiny and the §5.3 gap deserves a report.

Referee report

Significance

If correct, the local classification (2.52)-(2.58) is a genuinely general statement: every supersymmetric warped AdS5 x M6 background of D=11 supergravity with flux on M6 is locally of this form, with the flux fixed by the geometry rather than chosen. That is a strong structural result and it is supported by two independent derivations (the d=6 bilinear route and the d=7 SU(3) route of ref. [22]), which is exactly the kind of cross-check that makes a classification believable. The explicit closed-form families in sections 4 and 5 are a substantial byproduct: the positive-curvature KE family of section 4.1, the S2 x T2 family of section 5.1, and the reduction/T-duality chain leading to a new one-parameter family of Sasaki-Einstein spaces containing T^{1,1}/Z2 are all concrete and checkable. The paper also corrects a factor in the last equation of (2.19) as quoted in ref. [22], and Appendix D argues, with a stated reason (the Calabi-Yau assumption implicit in ref. [46]), that flux Minkowski5 vacua are possible, contrary to the earlier no-go claim. These are real contributions and the manuscript states its assumptions openly.

Major objections (2)

[Section 5.3 and abstract:s2] The abstract states the result unconditionally: 'We find a large family of new explicit regular solutions ... where the latter is either (i) Kahler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces.' For branch (i) the regularity argument is carried out in detail in section 4.1, including the explicit check that the conical-singularity coefficient alpha^2 of (4.9) equals one at both roots of the quartic (4.6). For branch (ii) the S2 x T2 case is worked out in section 5.1 with explicit ranges (0 < a < 1, c != 0) and an explicit c = 0 metric (5.8). But section 5.3, which covers the S2 x S2 and S2 x H2 bases with a1 != a2, only says 'for various ranges of (a1, a2, c) there are regular solutions' and 'the existence of regular solutions is rather easy to see if one sets c = 0'. No ranges are given, and no positivity or conical-singularity check is performed at the poles of the (y, psi) sphere. Since the non-Einstein S2 x S2 branch is precisely the part of branch (ii) that is not already contained in the KE analysis of section 4, this is the least-secured link in the headline claim. Either supply the explicit ranges of (a1, a2, c) together with the analogue of the alpha^2 = 1 check of section 4.1, or work out the c = 0 case in full, or qualify the abstract so that the unconditional phrasing matches what is actually demonstrated.
[Section 3.2 and abstract:s2] The exhaustiveness of the compact classification rests on Theorem 2 of ref. [35] and therefore on the Goldberg conjecture, as the authors state explicitly in section 3.2 ('assuming that the Goldberg conjecture is true'). The authors acknowledge this, so the caveat itself is not at issue. What remains is that the abstract's phrasing of the two-class split reads as unconditional, while the caveat appears only in the body. A one-clause qualification in the abstract, or a forward pointer from the abstract to section 3.2, would make the strength of the claim match its support without weakening the paper.

Minor objections (6)

[Eq. (4.15)] The type IIA metric in (4.15) reads 'y (dx1^2 + dx2^2 + dx3^3)'; the last term should presumably be dx3^2. Please check this and the parallel expressions in (5.9) and (5.10).
[Section 4.1] The statement that alpha^2 = 1 'for both y1 and y2 (in fact for all the roots of the quartic (4.6))' is asserted without showing the algebra. A short line of computation, or a footnote, would let the reader verify the smoothness of the CP1 fibre without redoing it.
[Section 2.2] The text notes that the last equation of (2.19) 'corrects that appearing in ref. [22] by a factor' but does not say which factor. Stating the corrected versus original expression explicitly would make the erratum useful to readers of ref. [22].
[Abstract and Section 5.2] The claim of a new family of Sasaki-Einstein spaces, and the flux-quantisation discussion in section 6, are both deferred to the companion paper ref. [38] (arXiv:hep-th/0403002). This is reasonable, but the abstract's phrasing 'a new family of Sasaki-Einstein spaces' would read more accurately if it made clear that the global analysis establishing regularity of the type IIB metrics is carried out in ref. [38] rather than here.
[Eq. (5.12)] The '1 <-> 2' shorthand in the flux expression is compact but easy to misread; spelling out the second term, or adding a sentence defining exactly which quantities are exchanged, would help.
[Section 2.1] The relation between zeta and alpha is given twice, as zeta = pi/2 - 2alpha and cos 2alpha = sin zeta, sin 2alpha = cos zeta. A single sentence fixing the sign convention once and for all would remove the need for the reader to reconcile the two.

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The paper

The paper claims

The authors derive the general local shape of any supersymmetric M-theory background that is a warped product of five-dimensional anti-de Sitter space with a six-dimensional internal space, and then solve the resulting equations explicitly,

The reading

The paper asks a classification question: if a solution of eleven-dimensional supergravity is a warped product of $AdS_5$ with a six-dimensional space $M_6$ and carries four-form flux on $M_6$, what shape must $M_6$ have in order to preserve at least one supersymmetry? The authors answer it locally. They show that $M_6$ always carries a Killing vector, and that the metric orthogonal to it is built from a one-parameter family of four-dimensional Kähler metrics whose complex structure does not vary along the family, together with a single angular function that also fixes the warp factor; the flux is then completely determined by the geometry, and the flux equation of motion and Bianchi identity come for free. Imposing that $M_6$ be a complex manifold collapses the remaining freedom enough that the equations can be integrated in closed form, producing families of explicit regular compact solutions in which a two-sphere is fibred over a four-dimensional Kähler base. The payoff is a supply of new candidate gravity duals of four-dimensional superconformal field theories, with the Killing vector playing the role of the R-symmetry, and a new route (via reduction and T-duality) to Sasaki-Einstein five-manifolds, including a known one, $T^{1,1}/Z_2$, as a special case.

What carries the argument

The engine is the translation of the eleven-dimensional Killing spinor equation into differential conditions on spinor bilinears, which define a local $SU(2)$ structure on $M_6$: a $(1,1)$-form $J$, a $(2,0)$-form $Omega$, and two one-forms $K^1$ and $K^2$. The conditions (2.13)–(2.16) on these forms are shown to be equivalent to the seven-dimensional $G$-structure conditions of the flux-compactification literature, which supplies the sufficiency argument and shows that the Bianchi identity and flux equation of motion follow from supersymmetry whenever $sinzeta$ is not identically zero. The bilinear $coszeta,K^2$ is shown directly from the Killing spinor equation to be a Killing vector, which is what allows coordinates $(x^i, y, psi)$ to be introduced and the metric to be put in the local form quoted above. The second piece of machinery is the reduction of the complex case to a single nonlinear ODE: integrability of the almost complex structure on $M_6$ forces $d_4zeta = d_4lambda = partial_y rho = 0$, after which the Ricci form of the base satisfies $hat{mathfrak{R}} = -frac{3}{2}y,partial_y hat J$, so the Ricci eigenvalues are constant on the base, and the remaining condition becomes one equation for $lambda(y)$ and $zeta(y)$ that is integrated explicitly in each case.

Extended reading notes

Core claim

The central claim is a local classification theorem plus an explicit solution-generating machine. On the classification side, the authors show that the necessary and sufficient conditions for a warped $AdS_5$ solution with internal flux are that the metric take the form $ds^2 = e^{-6lambda}(hat g_{ij}dx^idx^j + sec^2zeta,dy^2) + frac{1}{9m^2}cos^2zeta,(dpsi+rho)^2$, where $hat g$ is a family of four-dimensional Kähler metrics parameterised by $y$ with a complex structure independent of $y$ and $psi$, $rho$ is fixed by the Ricci-form connection of that Kähler metric together with the gradient of $logcoszeta$, and the warp factor and angle obey $2my = e^{3lambda}sinzeta$; the four-form is then given by equation (2.50) and is independent of $psi$. On the construction side, they specialise to complex $M_6$ and to the global ansatz in which $(y,psi)$ form a holomorphic $CP^1$ bundle over a smooth Kähler base, and they show that regularity plus the supersymmetry equations force the base, at fixed $y$, to be either Kähler-Einstein or a product of two constant-curvature Riemann surfaces. Solving the surviving ordinary differential equation gives three regular compact families: $CP^1$ bundles over positive-curvature Kähler-Einstein bases (which are $S^2times S^2$, $CP^2$, or $CP^2# n,CP^2$ with $n=3,ldots,8$) for a one-parameter range, and $S^2$ bundles over $S^2times T^2$ and over $S^2times S^2$. Non-compact regular families with $S^2times H^2$ bases are also found, and the earlier $N=1$ Maldacena–Núñez solution is recovered as a degenerate limit in which the fibre period is $4pi$ rather than $2pi$ and the total space is topologically an $S^4$ bundle over $H^2$.

Load-bearing premise

The claim that the regular compact solutions fall into exactly two classes, and no others, rests on the Goldberg conjecture, which the authors invoke explicitly when they apply a splitting theorem for compact Kähler four-manifolds whose Ricci tensor has two pairs of constant eigenvalues; if that conjecture fails for the relevant manifolds, the explicit solutions survive but the classification is no longer exhaustive.

Editorial extensions

If this is right

Every supersymmetric warped $AdS_5$ background of eleven-dimensional supergravity with flux on the internal space is locally of the form (2.51) with conditions (2.52)–(2.58), so the search for such backgrounds reduces to choosing a family of four-dimensional Kähler metrics and solving one ODE.
The regular compact solutions give concrete new M-theory duals of four-dimensional $N=1$ superconformal field theories, with the $partial/partialpsi$ Killing vector identified as the R-symmetry.
Reducing the $S^2times T^2$ family on one torus circle and T-dualising on the other produces type IIB solutions whose five-dimensional internal space is Sasaki-Einstein, giving a new one-parameter family that contains $T^{1,1}/Z_2$ as a special case.
The same analysis, run with the cosmological constant set to zero, characterises warped products of five-dimensional Minkowski space with $M_6$, including flux backgrounds that a Calabi–Yau-based no-go argument would have excluded.
Because the classical solutions come in continuous families, the authors expect flux quantisation to cut them down to a discrete, possibly countably infinite, subset of genuine string-theory backgrounds.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The classification is local, so the global reach of the result depends on a separate gluing analysis at the poles of the two-sphere and at any degeneration of the Kähler base; the paper checks this case by case, but a systematic treatment of simultaneous degeneration of base and fibre is left open, and the authors say so.
The one-parameter families are natural places to look for continuous deformations of the dual conformal field theory, for example as marginal or relevant operators whose couplings are the parameters $a$ and $c$; matching those parameters to gauge-theory data would be a concrete test of the proposed dualities.
Because the flux is fixed algebraically by the Kähler data rather than by a choice, the construction resembles a solution-generating transform: feeding in any Kähler–Einstein four-manifold of positive curvature yields a background, which suggests searching the Tian–Yau list for further explicit metrics and checking their flux quantisation.
The Minkowski-space appendix produces flux vacua that a Calabi–Yau ansatz would have ruled out, which is a hint that no-go arguments stated for restricted internal geometries should be re-examined rather than taken as general.

Original abstract

We analyse the most general supersymmetric solutions of D=11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M_6, with four-form flux on M_6. We show that M_6 is partly specified by a one-parameter family of four-dimensional Kahler metrics. We find a large family of new explicit regular solutions where M_6 is a compact, complex manifold which is topologically a two-sphere bundle over a four-dimensional base, where the latter is either (i) Kahler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T^{1,1}/Z_2. Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.

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The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,448 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.17 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We analyse the most general supersymmetric solutions of D=11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M_6, with four-form flux on M_6. We show that M_6 is partly specified by a one-parameter family of four-dimensional Kahler metrics. We find a large family of new explicit regular solutions where M_6 is a compact, complex manifold which is topologically a two-sphere bundle over a four-dimensional base, where the latter is either (i) Kahler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T^{1,1}/Z_2. Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We analyse the most general supersymmetric solutions of D=11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M_6, with four-form flux on M_6.	contribution 0.96	0.93	0.09	asserted 0.93
s1	We show that M_6 is partly specified by a one-parameter family of four-dimensional Kahler metrics.	result 0.99	0.95	0.23	asserted 1.00
s2	We find a large family of new explicit regular solutions where M_6 is a compact, complex manifold which is topologically a two-sphere bundle over a four-dimensional base, where the latter is either (i) Kahler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces.	result 0.97	0.97	0.57	asserted 1.00
s3	After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T^{1,1}/Z_2.	result 0.66	0.84	0.11	asserted 0.91
s4	Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.	result 0.74	0.87	0.05	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Forward citations

Cited by 50 Pith papers

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How later papers used it

115 later papers cite it

Evidence: substantial. 87 of the citing papers share no author with it, and 22 of those carry a confident label from Pith's citation classifier.

Pith read 39 of the 278 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

5 later papers by other authors are listed below: 2 built on it and 3 compared their own results with it. 2 more papers by the same authors are listed: 1 built on it and 1 compared its own results with it.

Builds on it 3 of 8 papers with this label · 1 by the same authors

Deformed the supergravity solutions given in this paper so that the resulting solutions have the Schrödinger symmetry.

Supersymmetric non-relativistic geometries in M-theory (2009) · 0.99 · paraphrased: the licence does not allow quoting
Showed how the solutions of this paper, which include the M-theory uplift of the Y_p,q and N=1 Maldacena and Núñez geometry, embed into this class.

Quarter-BPS AdS5 solutions in M-theory with a T2 bundle over a Riemann surface (2013) · 0.91 · paraphrased: the licence does not allow quoting

By the same authors

Considered the class of AdS_5×M_6 solutions of this paper, expanding and extending the discussion in another work.

Equivariant localization for AdS/CFT (2023) (same authors) · 0.99 · paraphrased: the licence does not allow quoting

Compares with it 4 of 12 papers with this label · 1 by the same authors

Found that, written in this form, its metric components are essentially identical to those of this paper.

Schrodinger invariant solutions of M-theory with Enhanced Supersymmetry (2009) · 1.00 · paraphrased: the licence does not allow quoting
Uplifted to 11d to compare with this paper.

Supersymmetric AdS$_{5}$ solutions of type IIB supergravity without D3 branes (2016) · 0.99 · paraphrased: the licence does not allow quoting
Being in massless IIA we can lift the solution of [ref] to $d=11$ to obtain AdS$_5 ×𝕎ℂℙ^2 ×𝕋^2$ of the form [equation] In this case the flux quantisation condition yields (upon sending $N_4→N_5$) [equation] Upon fixing $(k_1=k_2=1, k_3=2)$, this $d=11$ solution actually reproduces an AdS$_5×𝕋^2×𝕎ℂℙ^2_[1,1,2]$ solution from [ref] [We thank James Sparks and Jerome Gauntlett for bring this to our attention.].

Supersymmetric $\mathbb{WCP}^n$, AdS near horizons and orbifolds (2025) · AdS$_5×𝕎ℂℙ^2$ · 0.84

By the same authors

Gave the ESE form of the generic M-theory background, showing explicitly how the integrability conditions reproduce those given in this paper.

The exceptional generalised geometry of supersymmetric AdS flux backgrounds (2016) (same authors) · 0.84 · paraphrased: the licence does not allow quoting

How the literature uses it

112 arXiv papers cite this in 273 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 157 sentences without a confident label

Contests it 1 paper

The latter appears without derivation, so in the appendix we validate their claim by following a similar decomposition to that appearing in [ref] (see also [ref] )[We also cure some typos in [ref] .].

N = 2 SCFTs: An M5-brane perspective · Introduction · contest 0.78

Builds on it 8 papers

In this section, we will deform the supergravity solutions given in [ref] in such a way that the resulting solutions have the Schrödinger symmetry.

Supersymmetric non-relativistic geometries in M-theory · General consideration · 0.99
Next we show how the solutions of GMSW [ref] , which includes the M-theory uplift of the $Y_p,q$ [ref] and $𝒩=1$ Maldacena and Núñez geometry [ref] , embed into this class.

Quarter-BPS AdS5 solutions in M-theory with a T2 bundle over a Riemann surface · Class Ia · 0.91
We first consider the class of $AdS_5×M_6$ solutions of [ref] , expanding and extending the discussion in [ref] .

Equivariant localization for AdS/CFT · Introduction · 0.99

Uses its method or tool 11 papers

The utility of the coordinates of [ref] is now manifest.

Four-Dimensional SCFTs from M5-Branes · Supergravity solutions in canonical coordinates · 0.97
Following the same spinor decompositon as [ref] , $ϵ= ψ⊗e^λ/2 ξ$, it can be shown that imposing $ρ^+ ψ= 0$ kills all superconformal supersymmetry while preserving just two Poincaré supersymmetries.

NR $CFT_3$ duals in M-theory · Preliminaries · 0.95
To cast the geometry into the form of [ref] we first note that $K^1$ defines a canonical coordinate $Y$ through K^1= e^-3λ ζd[ - 1/3 m(y) x ] = e^-3λ ζdY , where e^λ= Δ^1/6 , sinζ= 2/3Δ^1/2 m(y) x .

New ${\cal N} = 1$ supersymmetric $AdS_5$ backgrounds in Type IIA supergravity · M-theory lift · 0.88

Uses its data or values 1 paper

In constructing an explicit example in this class we adopt the $SE_5$ metric discovered in [ref] ds^2_SE_5 = 1-cy/6(dθ^2+sin^2θdϕ^2)+e^-6λ^2ζdy^2 +19cos^2ζ(Dβ)^2 +e^6λ(dz+ac-2y+cy^2/6(a-y^2)Dβ)^2

Schrodinger invariant solutions of M-theory with Enhanced Supersymmetry · $S^2×T^2$ solution · 0.89

Compares with it 12 papers

Written in this form, the metric components we have found are essentially identical to those of [ref] .

Schrodinger invariant solutions of M-theory with Enhanced Supersymmetry · Solution · 1.00
Uplifting to 11d allows us to compare with [ref] .

Supersymmetric AdS$_{5}$ solutions of type IIB supergravity without D3 branes · Conclusions · 0.99
We then give the ESE form of the generic M-theory background, showing explicitly how the integrability conditions reproduce those given in [ref] .

The exceptional generalised geometry of supersymmetric AdS flux backgrounds · AdS5 backgrounds as ESE spaces · 0.84

Cites it as support 2 papers

If this happens at every point, we have a true global $3$ structure and one finds that supersymmetry is incompatible with the presence of flux [ref] .

Exceptional complex structures and the hypermultiplet moduli of 5d Minkowski compactifications of M-theory · Local SU(2) Structures · 0.96
These solutions are not supersymmetric: for $M_6=CP^3$ this was proved in [ref] , and for general $M_6$ it follows from the analysis of supersymmetric $AdS_5$ solutions of [ref] .

On the stability and spectrum of non-supersymmetric AdS(5) solutions of M-theory compactified on Kahler-Einstein spaces · Introduction · 0.97

Cites it as background 55 papers

Before dealing with non-relativistic solutions, let us describe the general $𝒩=1$ supersymmetric solutions of the supergravity limit of M-theory consisting of a warped product of $AdS_5$ and a six-dimensional space considered in [ref] .

Supersymmetric non-relativistic geometries in M-theory · Warped $AdS_5$ solutions in M-theory · 0.89
The necessary and sufficient conditions for supersymmetric $AdS_5$ solutions in M-theory are given in [ref] (GMSW system).

Quarter-BPS AdS5 solutions in M-theory with a T2 bundle over a Riemann surface · Supersymmetric $AdS_5$ systems in M-theory · 0.83
Before matching the previous solution within the classification in [ref] , let us briefly review the most general $= 1$ eleven dimensional solutions with an $AdS_5$ factor found in that paper.

The $AdS_5$ non-Abelian T-dual of Klebanov-Witten as a $\mathcal{N} = 1$ linear quiver from M5-branes · Review of GMSW · 0.99

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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