Supersymmetric AdS_3, AdS_2 and Bubble Solutions

Daniel Waldram; Jerome P. Gauntlett; Nakwoo Kim

REVIEW

Supersymmetric AdS_3, AdS_2 and Bubble Solutions

Jerome P. Gauntlett, Nakwoo Kim, Daniel Waldram

High Energy Physics - Theory · Submitted 22 Dec 2006 · 27 references

Pith's verdict: A solid construction paper: the new D=11 AdS2 family and the toric-like rescaling of superstar Kähler geometry are real results, but the §5 families never exhibit a regular member.

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CitationDaniel Waldram, Jerome P. Gauntlett, Nakwoo Kim. "Supersymmetric AdS_3, AdS_2 and Bubble Solutions." arXiv:hep-th/0612253 (2006). https://pith.science/paper/FKTSRXTF

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Bottom line: the framework is sound, the genuinely new pieces are in §3.2, §3.3 and §5, and the soft spot is narrower than the reader's report suggests — it sits in §5's global completion, not in the general construction or in flux quantisation. The abstract's claim [abstract:s0] is local existence of supergravity solutions, and that claim holds up on reading the derivations. J is closed by construction, the holomorphic form (3.4) gives integrability, and R = dP reproduces (1.1). Nothing circular here; the inputs from [1, 2] are published derivations, not smuggled assumptions. What is new and worth your time: the n=3 family (3.36), where the conical-singularity removal at both roots of q(y) works out identically — I checked (3.38) by hand and the identity q'(y_i)^2 = 16 y_i^3 (y_i^3 - 3y_i + 2a) does hold at any root — together with the explicit regular parameters (3.40)-(3.41). That is a complete, checkable result. The non-compact solutions (3.43) interpolating AdS4 x SE7 to the wrapped-membrane solution of [17] are a nice piece of geometry; the defect-CFT reading is offered as an interpretation and flagged as such, which is the right register. The idea in §5 — that the multi-charged superstar Kähler metric can be continued to R > 0 by the same rescaling trick that worked in the equal-charge case — is the actual insight, and it is a good one. What is rederived: §3.1 is [11] in different coordinates and §4 is the uplifted single-charged superstars of [21, 22, 25]. The paper says so plainly; these are consistency checks, not new physics. Where I part company with the reader: quantisation is a string/M-theory consistency condition the authors explicitly defer, and the abstract only claims supergravity solutions, so I would not weight it heavily. Positivity of (5.13) and (5.25) is manifest from the written form, so 'positivity only partially checked' is too strong. The real gap is that (5.14)-(5.17) and (5.26)-(5.28) are stated and never solved — unlike §3.2, §5 exhibits no explicit smooth compact member of either family. That is a genuine but contained gap, and the authors flag it. Who should read it: anyone working on wrapped-brane AdS backgrounds or bubbling geometries, and anyone hoping to import toric methods into this class. Send it out; the referee should press on §5 regularity and leave quantisation to a follow-up.

Referee report

Significance

If correct, the paper delivers genuinely new local supergravity backgrounds with holographic duals: a compact one-parameter D=11 AdS2 family, non-compact AdS2 backgrounds with a defect interpretation, and toric-like AdS3 and AdS2 families obtained from the superstar Kahler geometry. The structural observation that the wrapped-brane AdS3/AdS2 problem is governed by the same fourth-order scalar condition (1.1) that replaces the Einstein condition for Sasaki-Einstein cones is a useful organising principle, and the explicit matching to [11] in section 3.1 and to the uplifted single-charged superstars in section 4 provides real cross-checks rather than assertions. Credit is due for the explicit regularity analysis of the new D=11 family: the period-2pi choice in (3.38) does remove both conical singularities, and I verified by hand that q'(y_i)^2 = 16 y_i^3 (y_i^3 - 3 y_i + 2a) holds identically at any root of q(y) = y^4 - 4y^2 + 4ay - a^2, so that family is genuinely smooth. The manifestly positive-definite rewritings (5.13) and (5.25) are also a real improvement over a case-by-case check. The main shortfall is that the section 5 families are not shown to possess a single regular member

Major objections (2)

[Section 5.2 and Section 5.4, Eqs. (5.14)-(5.17) and (5.26)-(5.28)] The new AdS3 and AdS2 families (5.13) and (5.25) are presented as new solutions, but the regularity analysis stops at the conditions (5.14)-(5.17) and (5.26)-(5.28). The text asserts that the relation (5.17) 'then further restricts the parameters qi', yet no values of qi, of the integers (p,q,r_i), or of the range of w are exhibited that satisfy all five (respectively six) degeneration conditions at once. This is in sharp contrast with Section 3.2, where (3.40)-(3.41) give explicit parameter choices for the compact D=11 family, and with Section 6, where the product solutions are regular by inspection. Because smoothness at w = w1, w2 (respectively w2, w3) and at the three (four) points mu_i = 0 must be simultaneously compatible with 0 < F < 1, the existence of a smooth compact member of either family is not established. Please either exhibit at least one explicit regular member of each family, or give an argument that solutions of (5.17) and (5.28) exist, or state plainly that these are local families whose global completion is left open. The deferral of five-form and four-form quantisation in Sections 5.2 and 5.4 is acknowledged by the authors and is not itself a defect for a claim about supergravity solutions; the unexhibited regular member is the load-bearing gap.
[Section 3.2, Eqs. (3.39)-(3.41)] As displayed, Eq. (3.40) gives a = mq(2p+mq)(2p^2+2mpq+m^2q^2), a product of integers which for any q different from zero is of order unity or larger and grows with the integers, whereas the surrounding text requires 0 < a < 1 for q(y) to have four real roots and for the interval y2 <= y <= y3 to be non-degenerate. Since (3.39)-(3.41) are precisely what make Y9 a genuine U(1) bundle over the S^2 bundle over KE6 rather than a quotient, this inconsistency bears on the compactness claim for the headline D=11 family of (3.36). Please check the normalisation of (3.40) and (3.41); if the intended expression contains a denominator, as the analogous conditions in [11] do, the corrected form should be stated explicitly.

Minor objections (10)

[Section 4.2] The sentence 'When KE+4 = CP3 this is precisely the supersymmetric single-charged AdS4 black hole' should read KE+6 = CP^3, since the base in this subsection is six-dimensional.
[Section 5.4] The sentence 'We now have six different degenerations: the four points mu_i = 0 together with w = w1 and w = w2' is inconsistent with the stated range w2 <= w <= w3 and with (5.26), which runs over i = 2, 3; the two roots should be w = w2 and w = w3.
[Section 5.4] The condition 'require w2 <= w <= w3 with w3 > -q1' should presumably read w2 > -q1, since positivity of (5.25) requires w + q_i > 0 for every i and q1 is the smallest of the q_i; this is exactly how the analogous condition is written in Section 5.2.
[Section 5.1, Eq. (5.8)] With f = 1 + r^2 H and H = H1 H2 H3 as defined in (5.3), one has r^2 + H^{-1} = f/H, not fH; please check the last equality in (5.8).
[Section 5.2] The statement that the metric (5.1) 'satisfies (1.1) with Ricci scalar R = -DHr^4' is inconsistent with e^{4A} = DHr^4 in (5.1) together with R = -8 e^{-4A} from Section 2.2, and is dimensionally not a Ricci scalar; presumably the intended expression is R = -8/(DHr^4). Please verify.
[Section 6.4, Eq. (6.18)] As displayed, the fourth entry of the tuple depends only on l1 and l2, which does not satisfy the constraint (6.3) for generic l3; comparison with (6.16) and (6.19) suggests the intended expression is l4 = -(l1 l2 + l1 l3 + l2 l3)/(l1 + l2 + l3). Please check, since the claimed two-parameter family depends on it.
[Section 5.2 and Section 5.4] The symbol F is used both for the two-form that determines the flux in (2.4) and (2.9) and for the function F(w) introduced in (5.11) and (5.23); a different letter for the latter would avoid ambiguity.
[Section 3.1] The assertion that the six-dimensional Kahler leaves 'necessarily' have conical singularities at one of the poles is stated without argument; a sentence explaining why the period of phi cannot be chosen to remove both singularities would help the reader.
[Section 6.3] The sentence 'R > 0 implies that l4 >= 0' should read l4 > 0, since R = 2(l1+l2+l3+l4) with l1 <= l2 <= l3 <= l4.
[Sections 2.2, 3.2, 5.2, 6.2] Several typographical slips should be corrected: 'the AdS solutions discussed thus can' (Section 2.2), 'we need ensure' (Section 3.2), 'let us instead examineds2(Y7)' (Section 5.2), and 'four-dimesnional Bergmann metric' (Section 6.2).

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The paper

The paper claims

A single fourth-order equation on a Kähler metric generates new supersymmetric $AdS_3$ solutions in type IIB and $AdS_2$ solutions in $D=11$ supergravity, with the sign of the Ricci scalar switching between AdS and bubble backgrounds.

The reading

The paper asks whether one local geometric condition can act as a factory for supersymmetric anti-de Sitter backgrounds in string and M-theory. Its answer is that a Kähler metric on a $2n+2$-dimensional space satisfying $$(1.1)$$ determines the internal geometry of both type IIB $AdS_3$ and $D=11$ $AdS_2$ solutions, with the flux fixed by the same Kähler data. The sign of the Ricci scalar decides the physical use: $R>0$ gives an $AdS$ factor, while $R<0$ gives a bubble geometry with an $S^3$ or $S^2$ factor. The authors then exhibit three ways to manufacture such metrics: an $S^2$ fibration over a positively curved Kähler-Einstein space, a rescaling of the Kähler geometry hidden in multi-charged superstar solutions, and a product of two-dimensional Kähler-Einstein spaces. If the construction holds up globally, it gives new holographic backgrounds for two-dimensional $(0,2)$ CFTs, conformal quantum mechanics, defect CFTs, and BPS bubble states.

What carries the argument

The load-bearing object is a Kähler metric (a metric whose associated two-form is closed) on a $2n+2$-dimensional space whose Ricci scalar and Ricci tensor satisfy $$(1.1)$$. In the $AdS_3$ case ($n=2$) the internal seven-manifold is $ds^2(Y_7)=1/4(dz+P)^2+e^{-4A}ds^2_6$ with $dP=R$ and $e^{-4A}=1/8R$; in the $AdS_2$ case ($n=3$) the internal nine-manifold is $ds^2(Y_9)=(dz+P)^2+e^{-3A}ds^2_8$ with $e^{-3A}=1/2R$. The Kähler condition makes the flux closed, and (1.1) makes the equation of motion hold, so the whole supergravity solution is reduced to finding a Kähler metric with the right sign of $R$. The paper's three constructions are concrete ways to solve that one equation: an $S^2$ fibration with metric $ds^2_{2n+2}=dρ^2/U+Uρ^2(Dφ)^2+ρ^2ds^2(KE^+_{2n})$, a rescaling of the multi-charged superstar Kähler metrics, and a direct product of two-dimensional Kähler-Einstein metrics.

Extended reading notes

Core claim

The central claim is that the fourth-order scalar condition $$(1.1)$$ is the right organizing equation for a broad class of supersymmetric $AdS_3$ and $AdS_2$ solutions, not just a technical consistency condition for one example. Starting from a warped product with an internal space built over a $2n+2$-dimensional Kähler metric, the authors show that the warp factor and the five-form or four-form flux are fixed by that metric, and that the only remaining equation is (1.1). They then produce explicit solutions: the six-dimensional case recovers the known type IIB $AdS_3$ family of [11], the eight-dimensional case gives a new one-parameter $D=11$ $AdS_2$ family, a non-compact limit gives $AdS_2$ backgrounds dual to three-dimensional $N=2$ SCFTs with point-like defects, and rescaled multi-charged superstar metrics give new $AdS_3$ and $AdS_2$ families with toric-like isometries. The paper also shows that the same metrics with $R<0$ yield bubble solutions, including uplifts of single-charged superstars and new product-of-Kähler-Einstein bubbles. The claim is primarily a local geometric construction; global regularity and flux quantisation are checked only in part and are explicitly left for future work in several families.

Load-bearing premise

The load-bearing premise is that the local Kähler metrics satisfying (1.1) can be completed to smooth compact internal spaces with properly quantised five-form or four-form flux; the paper checks regularity in places but explicitly postpones flux quantisation for the $D=11$ fibration family and for the new multi-charged $AdS$ families.

Editorial extensions

If this is right

The type IIB $AdS_3$ solutions have dual two-dimensional $(0,2)$ SCFTs, and the $D=11$ $AdS_2$ solutions have dual conformal quantum mechanics with two supercharges.
The non-compact $AdS_2$ solutions are dual to three-dimensional $N=2$ SCFTs coupled to point-like defects.
The bubble solutions describe BPS states in the dual conformal theories and preserve four supersymmetries.
The fibration construction recovers the known $AdS_3$ family of [11] and produces a new one-parameter $D=11$ $AdS_2$ family.
The product-of-Kähler-Einstein construction includes near-horizon geometries of D3-branes wrapping a holomorphic curve in a Calabi-Yau four-fold and M2-branes wrapping a holomorphic curve in a Calabi-Yau five-fold.

Reading between the lines

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

If flux quantisation can be arranged, the continuous parameters in the multi-charged families will be discretised by integrality, giving a countable family of dual CFTs rather than a continuum.
The defect interpretation suggests a direct holographic computation of defect central charge or entropy from the non-compact $AdS_2$ metric, which the paper does not attempt.
The same fourth-order condition may serve as a classification tool for near-horizon geometries of wrapped branes beyond the explicit fibration, superstar, and product constructions.
A useful stress test is to compare the product-of-Kähler-Einstein solutions with known wrapped-brane central charges; agreement would tie the new families to specific CFTs.

Original abstract

We present new supersymmetric AdS_3 solutions of type IIB supergravity and AdS_2 solutions of D=11 supergravity. The former are dual to conformal field theories in two dimensions with N=(0,2) supersymmetry while the latter are dual to conformal quantum mechanics with two supercharges. Our construction also includes AdS_2 solutions of D=11 supergravity that have non-compact internal spaces which are dual to three-dimensional N=2 superconformal field theories coupled to point-like defects. We also present some new bubble-type solutions, corresponding to BPS states in conformal theories, that preserve four supersymmetries.

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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.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.68 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We present new supersymmetric AdS_3 solutions of type IIB supergravity and AdS_2 solutions of D=11 supergravity. The former are dual to conformal field theories in two dimensions with N=(0,2) supersymmetry while the latter are dual to conformal quantum mechanics with two supercharges. Our construction also includes AdS_2 solutions of D=11 supergravity that have non-compact internal spaces which are dual to three-dimensional N=2 superconformal field theories coupled to point-like defects. We also present some new bubble-type solutions, corresponding to BPS states in conformal theories, that preserve four supersymmetries.

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 present new supersymmetric AdS_3 solutions of type IIB supergravity and AdS_2 solutions of D=11 supergravity.	contribution 0.97	0.96	0.63	asserted 1.00
s1	The former are dual to conformal field theories in two dimensions with N=(0,2) supersymmetry while the latter are dual to conformal quantum mechanics with two supercharges.	interpretation 0.96	0.45	0.17	asserted 1.00
s2	Our construction also includes AdS_2 solutions of D=11 supergravity that have non-compact internal spaces which are dual to three-dimensional N=2 superconformal field theories coupled to point-like defects.	contribution 0.56	0.93	0.14	asserted 1.00
s3	We also present some new bubble-type solutions, corresponding to BPS states in conformal theories, that preserve four supersymmetries.	contribution 0.91	0.95	0.15	asserted 1.00

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

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sources read

arXiv listing abstract v2

not examined

full text
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levels run

P abstract

not run

S sections
T body sentences
C citations
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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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A new AdS3/CFT2 holographic duality is proposed between massive Type IIA backgrounds with N=(0,4) supersymmetry and two-row quiver gauge theories, supported by a leading-order match of central charges.
Wrapped Brane Solutions in Romans $F(4)$ Gauged Supergravity
hep-th 2019-09 conditional novelty 6.0 of 10

Wrapped D4-branes in Romans F(4) gauged supergravity are mapped to supersymmetric and non-supersymmetric AdS vacua, with new non-BPS AdS2 solutions whose stability is checked against the Breitenlohner-Freedman bound.
Aspects of AdS$_2$ classification in M-theory: Solutions with mesonic and baryonic charges
hep-th 2019-08 conditional novelty 6.0 of 10

The paper gives necessary and sufficient geometric conditions for N=(1,0) AdS2 solutions in M-theory with SU(4)-structure, and presents numerical evidence for a new Q^{1,1,1} solution with both mesonic and baryonic charges.
Toric geometry and the dual of ${\cal I}$-extremization
hep-th 2019-04 conditional novelty 6.0 of 10

A master volume formula for toric Calabi-Yau fourfolds yields an off-shell entropy function for AdS2 x Y9 and an off-shell central charge for AdS3 x Y7, reproducing known supergravity and field theory results from tor...
Toric geometry and the dual of $c$-extremization
hep-th 2018-12 accept novelty 6.0 of 10

A master volume formula on toric Calabi-Yau cones computes the central charge and BPS R-charges of the dual AdS3 (0,2) SCFTs from toric data and twist integers alone.
AdS$_3$ solutions with exceptional supersymmetry
hep-th 2018-07 accept novelty 6.0 of 10

Two locally unique type IIA supergravity solutions realize the exceptional F(4) and G(3) superalgebras on AdS3, with a round S6 fibred over an interval and an O8-plane at one end, plus numerical N=1 solutions with G2 ...
F-theory and AdS_3/CFT_2 (2,0)
hep-th 2017-12 conditional novelty 6.0 of 10

Varying the Type IIB axio-dilaton over the internal space yields new AdS3 solutions dual to 2d (0,2) SCFTs, with holographic and field-theory central charges agreeing to subleading order in N.
A Universal Counting of Black Hole Microstates in AdS$_4$
hep-th 2017-07 accept novelty 6.0 of 10

For a large class of 3d N=2 SCFTs with a universal topological twist, the planar-limit twisted index equals (g-1) times the three-sphere free energy, matching the entropy of a universal magnetically charged AdS4 black hole.
F-theory and AdS_3/CFT_2
hep-th 2017-05 accept novelty 6.0 of 10

The paper constructs the first AdS3 solutions of Type IIB supergravity with a genuinely varying axio-dilaton and shows their holographic central charges match field-theory and anomaly computations.
Two-dimensional SCFTs from D3-branes
hep-th 2015-11 accept novelty 6.0 of 10

Twisted compactification of 4d N=1 Y^{p,q} quivers on a Riemann surface gives 2d N=(0,2) SCFTs whose central charge is (32/3)(g-1) times the 4d a-anomaly, matched by explicit AdS3 solutions of IIB supergravity.
Two-dimensional SCFTs from wrapped branes and c-extremization
hep-th 2013-02 accept novelty 6.0 of 10

c-extremization fixes the exact R-symmetry and central charges of 2d N=(0,2) SCFTs from wrapped branes, and the results match independently built AdS3 supergravity duals.
Exact half-BPS string-junction solutions in six-dimensional supergravity
hep-th 2011-07 conditional novelty 6.0 of 10

The most general half-BPS AdS2 x S2-warped solution of six-dimensional (0,4) supergravity is derived in closed form, and its globally regular branch with N asymptotic AdS3 x S3 regions is parametrized explicitly by 2(...
Geometries with Killing Spinors and Supersymmetric AdS Solutions
hep-th 2007-10 accept novelty 6.0 of 10

The authors introduce a new class of complex geometries in 2n+2 dimensions with a Killing spinor, show their cone reduction gives 2n+1 dimensional geometries generalizing the known 7d and 9d cases, and construct infin...
Near-horizon geometries of supersymmetric AdS(5) black holes
hep-th 2007-08 accept novelty 6.0 of 10

Under the assumption of two rotational symmetries, supersymmetric asymptotically AdS5 black holes in U(1)^3 gauged supergravity can have only three horizon topologies: a sphere, a ring (S^1 x S^2), or a torus.
A tale of (M)2 twists
hep-th 2021-12 conditional novelty 5.0 of 10

Both twist and anti-twist AdS2 x spindle solutions exist in 4-charge STU supergravity, with closed-form free energies written directly in terms of magnetic charges and orbifold weights.
M2-branes on Discs and Multi-Charged Spindles
hep-th 2021-10 conditional novelty 5.0 of 10

The paper gives a complete global analysis of multi-charge AdS2 solutions from wrapped M2-branes on spindles and discs, and derives an entropy formula for the dual black hole.
${\cal N}=(2,2)$ AdS$_3$ from D3-branes wrapped on Riemann surfaces
hep-th 2021-07 conditional novelty 5.0 of 10

New N=(2,2) supersymmetric AdS3 solutions of type IIB supergravity are built from D3-branes on Riemann surfaces, and their central charge matches the dual field theory for hyperbolic surfaces.
Twisted D3-brane and M5-brane compactifications from multi-charge spindles
hep-th 2021-04 accept novelty 5.0 of 10

Multi-charge AdS3 supergravity solutions from branes wrapped on spindles have central charges and R-symmetries that agree with dual field theory computations via anomaly polynomials and c-extremization.
Rotating multi-charge spindles and their microstates
hep-th 2021-04 conditional novelty 5.0 of 10

Rotating dyonic spindle black strings in AdS5 x S5 have entropy that matches the charged Cardy formula computed from the two-dimensional anomaly polynomial obtained by integrating the four-dimensional N=4 SYM anomaly ...
AdS$_{\textbf{2}}$ solutions and their massive IIA origin
hep-th 2018-11 conditional novelty 5.0 of 10

New supersymmetric AdS2 x S3 x S-tilde3 warped solutions of massive IIA supergravity are derived from F(4) gauged supergravity and matched to a D0-F1-D4'-D4-D8 brane intersection.
Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity
hep-th 2007-04 accept novelty 5.0 of 10

BPS geometries of IIB supergravity with 1/4 and 1/8 supersymmetry are argued to be encoded by droplet-shaped regions excised from a curved Kähler base, generalizing the LLM 1/2 BPS picture.
Electrostatic Description of Five-dimensional SCFTs
hep-th 2021-04 conditional novelty 4.0 of 10

A convex piecewise-linear rank function fixed by Page charge quantisation encodes the quiver data of five-dimensional SCFTs, and the resulting backgrounds reproduce known central charges and Wilson loops.
3D Supergravity from wrapped D3-branes
hep-th 2013-07 conditional novelty 4.0 of 10

Wrapped-D3-brane AdS3 solutions are matched to three-dimensional gauged supergravities whose T tensor reproduces the exact central charge and R symmetry via c-extremization.
D3-branes and M5-branes wrapped on a topological disc
hep-th 2021-08 conditional novelty 3.0 of 10

Supersymmetric AdS3 solutions from D3-branes and M5-branes wrapped on a topological disc are constructed, uplifted to ten and eleven dimensions, and shown to have finite holographic central charge for the N=(2,2) case.

How later papers used it

70 later papers cite it

Evidence: substantial. 49 of the citing papers share no author with it, and 11 of those carry a confident label from Pith's citation classifier.

Pith read 23 of the 203 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

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

Builds on it 3 of 10 papers with this label · 3 by the same authors

By the same authors

Completed the analysis of flux quantization for solutions that this paper had constructed.

Fibred GK geometry and supersymmetric $AdS$ solutions (2019) (same authors) · 0.88 · paraphrased: the licence does not allow quoting
Generalized this paper's solutions by an extra rotation parameter, uplifting to regular AdS_2×Y_9 solutions.

Accelerating Black Holes and Spinning Spindles (2020) (same authors) · 0.99 · paraphrased: the licence does not allow quoting
Extended this paper's results by carrying out the analysis of flux quantization for the AdS_2×Y_9 solutions.

Toric geometry and the dual of ${\cal I}$-extremization (2019) (same authors) · 0.99 · paraphrased: the licence does not allow quoting

Uses its method or tool 2 of 7 papers with this label

Used the results in this paper to rewrite the metric in a form with the R-symmetry vector manifest.

M2-branes on Discs and Multi-Charged Spindles (2021) · 0.81 · paraphrased: the licence does not allow quoting
Wrote the AdS_3 metric as a foliation by AdS_2 as in this paper to perform the duality chain.

F-theory and AdS_3/CFT_2 (2,0) (2017) · 0.91 · paraphrased: the licence does not allow quoting

Compares with it 3 of 10 papers with this label · 2 by the same authors

Verified that its own metric is the same as that given in section 5.2 of this paper, identifying coordinates and parameters.

Twisted D3-brane and M5-brane compactifications from multi-charge spindles (2021) · 0.93 · paraphrased: the licence does not allow quoting

By the same authors

Once we identify $v_1$ in the metric [ref] and the flux [ref] as v_1=√(3ℓ_12+ℓ_1), we reproduce the metric and the flux in [ref] [Here we denote $L$ used in [ref] by $L_GKW$.

Uplifting dyonic AdS$_4$ black holes on seven-dimensional Sasaki-Einstein manifolds (2020) (same authors) · Comparison to known AdS$_2$ solutions · 0.98
Found its own black hole horizon metric to be precisely the metric of the AdS_2 solution constructed directly as in (6.15) of this paper, with length normalization as in this paper.

A geometric dual of $c$-extremization (2018) (same authors) · 0.93 · paraphrased: the licence does not allow quoting

How the literature uses it

68 arXiv papers cite this in 201 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 · 118 sentences without a confident label

Contests it 3 papers

The uplift formula, [ref] , is given for the metric, [equation] and for the self-dual five-form flux, $F_(5) = G_(5)+*G_(5)$,[A sign error in the second term of the formula in [ref] is corrected in [ref] and [ref] .] [equation] where we define [equation] and $vol_5$ and $*_5$ denote the volume form and the Hodge dual with respect to the five-dimensional metric, $ds_5^2$, respectively.

D3-branes and M5-branes wrapped on a topological disc · Uplift to type IIB supergravity · contest 0.76
Any supersymmetric solution of this model can be uplifted on $S^5$ to give a supersymmetric solution of type IIB supergravity using the results of [ref] .[As pointed out in [ref] there is a typo in the five-form flux in [ref] .

Supersymmetric spindles · The $D=5$ gauged supergravity model · contest 0.80
As in [ref] we have corrected the sign of the second factor in [ref], compared with the expression given in [ref] .

Twisted D3-brane and M5-brane compactifications from multi-charge spindles · Local form of the solutions · contest 0.81

Builds on it 10 papers

These uplift to regular $AdS_2×Y_9$ solutions, which generalise those of [ref] by an extra rotation parameter.

Accelerating Black Holes and Spinning Spindles · Near horizon limit: $AdS_2×𝕎ℂℙ^1_[n_-,n_+]$ · 0.99
This solution was obtained by taking the Baryonic twist solution for $Y^p,q$ found in [ref] and further elucidated in [ref] and performing a beta deformation [ref] along the two directions of the two-torus in the geometry.

$\mathcal{N}=(0,2)$ AdS$_3$ Solutions of Type IIB and F-theory with Generic Fluxes · A representative solution of the general case · 0.92
We also showed how the general class of $AdS$ solutions can be analytically continued to obtain general classes of 1/8 BPS bubble solutions with additional fluxes to the classes of solutions considered in [ref] .

AdS Solutions Through Transgression · Conclusions · 1.00

Uses its method or tool 7 papers

With these ingredients to hand, and using [ref] [equation] where $R$ is the Ricci scalar of the eight-dimensional transverse Kähler metric, we may now compute the “entropy" given by [ref] (see equation (2.20) of [ref] ) [equation]

Fibred GK geometry and supersymmetric $AdS$ solutions · $D=11$: $𝒴^,(KE_6^+)$ · 0.88
This is defined as a certain bilinear in the Killing spinors on $Y_7$ [ref] , and combining the general results of the latter reference with the form of the solution given in [ref] we can read off that this vector field is simply [equation] Here we have normalized the R-symmetry so that the Killing spinor on $Y_7$ has unit charge under the Lie derivative along this vector field, giving an explicit phase dependence of $^ϕ$.

Twisted D3-brane and M5-brane compactifications from multi-charge spindles · Central charge and R-symmetry · 0.89
We will also construct rich new classes of explicit solutions by following a similar analysis to that of [ref] .

AdS Solutions Through Transgression · Introduction · 0.95

Compares with it 10 papers

We show that this uplifted solution is equivalent to the eleven-dimensional solutions [ref] up to overall scaling.

Black holes with baryonic charge and $\mathcal{I}$-extremization · Uplift of $D=4$ solutions with baryonic magnetic charge · 0.98
We will show that the uplifts of magnetic, dyonic black holes correspond to AdS$_2$ solutions in M-theory with electric and dyonic baryonic fluxes, respectively, studied in [ref] .

Uplifting dyonic AdS$_4$ black holes on seven-dimensional Sasaki-Einstein manifolds · Uplifted AdS$_2$ solutions in $D=11$ supergravity · 0.83
One can verify that this is the same metric as that given in section 5.2 of [ref] , where we identify their coordinates and parameters, in terms of those presented here, as $w=x-α$, $z=-2ϕ$, $q_I=α+3K_I$.

Twisted D3-brane and M5-brane compactifications from multi-charge spindles · Local form of the solutions · 0.93

Cites it as background 29 papers

An interesting class of geometries in seven and nine dimensions was recently discovered in [ref] and further explored in [ref] .

Geometries with Killing Spinors and Supersymmetric AdS Solutions · Introduction · 0.89
In this section, we review AdS$_2$ solutions in $D=11$ supergravity, which were studied in [ref] by considering M2-branes wrapped on two-cycles in a Calabi-Yau 5-fold and further developed in [ref] .

Uplifting dyonic AdS$_4$ black holes on seven-dimensional Sasaki-Einstein manifolds · AdS$_2$ solutions in $D=11$ supergravity · 0.98
These solutions were first discussed in section 3.2 of [ref] , including determining the conditions required to obtain regular solutions, which are labelled by two positive, relatively prime integers, $,>0$.

Fibred GK geometry and supersymmetric $AdS$ solutions · $D=11$: $𝒴^,(KE_6^+)$ · 0.83

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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