arxiv: 2604.09137 · v2 · submitted 2026-04-10 · ✦ hep-th

Recognition: 2 theorem links

· Lean Theorem

Consistent Truncations from Duality Symmetries and Desingularization of Orbifold Uplifts

Anik Rudra , Colin Sterckx , Mario Trigiante

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:57 UTC · model grok-4.3

classification ✦ hep-th

keywords consistent truncationsgauged supergravityspindle solutionstype IIB upliftorbifold singularitiesduality symmetriesAdS solutionsregularity criterion

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The pith

G_S-invariant subsectors yield consistent truncations even without being symmetries, and type IIB spindle uplifts are always non-regular with eight codimension-six orbifold singularities.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that subsectors of maximal gauged supergravities preserved by a duality group G_S can serve as consistent truncations even when G_S does not preserve the full parent theory. This method is used to construct an N=4 subsector from the N=8 D=4 gauged supergravity and to build pure supergravities around supersymmetric AdS_D solutions. The same construction produces the type IIB uplift of multicharge spindle solutions, where a simple regularity criterion proves that every such uplift is non-regular and contains exactly eight codimension-six orbifold singularities. The criterion recovers known results for other spindles and makes predictions for those on quasi-regular Sasaki-Einstein seven-manifolds.

Core claim

G_S-invariant subsectors of maximal gauged supergravities provide consistent truncations even when G_S is not a symmetry of the original theory. This enables the construction of an N=4 subsector of the D=4 N=8 [SO(6)×SO(1,1)]⋉R^{12} gauged supergravity, which is then used to uplift multicharge spindle solutions to type IIB. A regularity criterion for the uplift shows that these geometries are always non-regular and admit eight codimension-six orbifold singularities.

What carries the argument

The G_S-invariant subsector that supplies a consistent truncation together with the regularity criterion that detects orbifold singularities in the type IIB uplift.

If this is right

Pure supergravities can be constructed around supersymmetric AdS_D solutions via these truncations.
Every type IIB uplift of a multicharge spindle is non-regular and contains eight codimension-six orbifold singularities.
The regularity criterion recovers known results for other spindle uplifts and predicts regularity properties for spindles on quasi-regular SE_7 manifolds.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The fixed count of eight singularities points to a universal orbifold structure in these uplifts.
The truncation technique may extend to other duality groups and dimensions where full symmetries are absent.

Load-bearing premise

That G_S-invariant subsectors of maximal gauged supergravities remain consistent truncations even when G_S is not itself a symmetry of the full supergravity.

What would settle it

An explicit substitution of the truncated fields into the full ten-dimensional equations of motion that produces a nonzero residual, or the construction of a spindle uplift in type IIB whose geometry is regular everywhere.

read the original abstract

This paper is an extension of the results presented in \cite{Guarino:2024gke}. We study $ G_S$-invariant subsectors of maximal gauged supergravities and show that such models can provide consistent truncations even when $G_S$ is not a symmetry of the original supergravity. We show that this construction is key to building pure supergravities around a supersymmetric AdS$_D$ solution. We illustrate this construction by building a consistent $\mathcal{N}=4$ subsector of the $D=4$ $\mathcal{N}=8$ $[\mathrm{SO}(6)\times \mathrm{SO}(1,1)]\ltimes \mathbb{R}^{12}$ gauged supergravity. We use this result to build the uplift of the multicharge spindle solutions in type IIB and we define a simple criterion for assessing the regularity of the uplift. We show that the type IIB uplift of the spindle is always non-regular, admitting eight codimension-six orbifold singularities. We apply the same criterion to other spindle uplifts, recovering known results and making predictions on the regularity of spindles on (quasi-)regular SE$_7$ manifolds.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows how to build consistent truncations from G_S-invariant subsectors even when G_S is not a symmetry, then uses that to prove type IIB spindle uplifts are always non-regular with exactly eight codimension-six singularities.

read the letter

The core result is a practical extension of truncation methods: G_S-invariant subsectors of maximal gauged supergravities can still give consistent truncations even if G_S is not a symmetry of the full theory. They demonstrate this by constructing an N=4 subsector of the D=4 N=8 [SO(6)×SO(1,1)]⋉R^{12} gauged supergravity, then apply it to define the uplift ansatz for multicharge spindle solutions in type IIB. From there they introduce a simple regularity criterion and conclude that every such uplift has eight codimension-six orbifold singularities. They also check the criterion against other known spindle uplifts and offer predictions for spindles on (quasi-)regular SE_7 manifolds. This is a direct, usable technical step for people who need to truncate and check regularity in AdS compactifications. The truncation construction and the regularity criterion are the parts that feel new and potentially reusable. The non-regularity claim for the type IIB spindle follows once the truncation is accepted and the criterion is applied. The main soft spot is the justification for the truncation itself when G_S is not a symmetry. The abstract states they prove consistency, but the strength of the result hinges on whether the equations of motion and supersymmetry variations actually close under the projection for the spindle backgrounds; any gap there would weaken the uplift and the singularity count. The paper cites the prior work it extends and does not appear to introduce free parameters or circular steps. It is aimed at researchers working on gauged supergravities, consistent truncations, and string uplifts of AdS solutions. Anyone already using similar subsector methods or checking regularity of orbifold uplifts will find the criterion and the explicit non-regularity result worth reading. It is solid enough on its own terms to deserve a serious referee, with the main questions likely centering on the truncation consistency proof and explicit checks against the original supergravity equations.

Referee Report

1 major / 1 minor

Summary. The paper extends prior results on consistent truncations by showing that G_S-invariant subsectors of maximal gauged supergravities yield consistent truncations even when G_S is not a symmetry of the parent theory. It constructs an explicit N=4 subsector of the D=4 N=8 [SO(6)×SO(1,1)]⋉R^{12} gauged supergravity, uses this to define an uplift ansatz for multicharge spindle solutions in type IIB, introduces a regularity criterion for the uplifted geometry, and concludes that all such type IIB spindle uplifts are non-regular with exactly eight codimension-six orbifold singularities. The same criterion is applied to other spindle uplifts on (quasi-)regular SE_7 manifolds to recover known results and generate new predictions.

Significance. If the truncation consistency proof holds, the work supplies a general method for extracting pure supergravities around AdS_D vacua via duality symmetries and supplies a practical regularity test for orbifold uplifts. The specific claim of eight codimension-six singularities in every type IIB spindle uplift, together with the predictions for SE_7 cases, would be a concrete, falsifiable statement about the geometry of these solutions.

major comments (1)

[Construction of the N=4 subsector and uplift ansatz] The central claim that the type IIB uplift is always non-regular with eight codimension-six singularities rests on the construction of a consistent N=4 truncation where G_S need not be a symmetry of the original N=8 theory. The manuscript must explicitly verify that the equations of motion and supersymmetry variations close under the G_S projection for the multicharge spindle backgrounds; any gap here would invalidate the uplift ansatz and the subsequent regularity analysis.

minor comments (1)

[Abstract and introduction] The abstract and introduction should clarify the precise relation to the cited prior work (Guarino:2024gke) so that the novel extension of the truncation theorem is immediately visible.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comment on the consistency of the N=4 truncation. We address the point below and will revise the paper accordingly to strengthen the presentation.

read point-by-point responses

Referee: [Construction of the N=4 subsector and uplift ansatz] The central claim that the type IIB uplift is always non-regular with eight codimension-six singularities rests on the construction of a consistent N=4 truncation where G_S need not be a symmetry of the original N=8 theory. The manuscript must explicitly verify that the equations of motion and supersymmetry variations close under the G_S projection for the multicharge spindle backgrounds; any gap here would invalidate the uplift ansatz and the subsequent regularity analysis.

Authors: We thank the referee for highlighting this point. The manuscript presents a general proof that any G_S-invariant subsector of the N=8 theory yields a consistent truncation, by showing that both the equations of motion and the supersymmetry variations remain closed under the projection (see Section 3). This argument does not rely on G_S being a symmetry of the parent theory and therefore applies to any solution lying in the subsector, including the multicharge spindle backgrounds. Nevertheless, we agree that an explicit substitution of the spindle ansatz into the truncated equations would make the application more transparent. In the revised manuscript we will add a short subsection performing this verification for the spindle metric and fluxes, confirming that the projected EOM and SUSY variations are satisfied. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation of truncation extension, uplift, and regularity criterion is self-contained

full rationale

The paper derives that G_S-invariant subsectors can yield consistent truncations even when G_S is not a symmetry of the original supergravity, illustrates the result by explicitly constructing the N=4 subsector of the D=4 N=8 [SO(6)×SO(1,1)]⋉R^{12} gauged supergravity, uses it to define the type IIB uplift ansatz for multicharge spindles, introduces a regularity criterion, and concludes that the uplift is always non-regular with exactly eight codimension-six orbifold singularities. The reference to prior work is contextual; the central steps are new constructions and proofs presented in this manuscript. No self-definitional loops, fitted parameters renamed as predictions, or load-bearing self-citations that reduce the main claims to unverified inputs appear in the provided text. The chain from truncation consistency to uplift to regularity assessment stands independently against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central construction rests on the domain assumption that G_S-invariant subsectors remain consistent truncations without being symmetries; no free parameters or new invented entities are mentioned in the abstract.

axioms (1)

domain assumption G_S-invariant subsectors of maximal gauged supergravities can provide consistent truncations even when G_S is not a symmetry of the original supergravity
This is the key extension stated in the abstract that enables all subsequent constructions.

pith-pipeline@v0.9.0 · 5517 in / 1367 out tokens · 24521 ms · 2026-05-10T17:57:22.772242+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We show that the type IIB uplift of the spindle is always non-regular, admitting eight codimension-six orbifold singularities.
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

G_S-invariant subsectors ... even when G_S is not a symmetry of the original supergravity

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

74 extracted references · 68 canonical work pages · 1 internal anchor

[1]

Guarino, C

A. Guarino, C. Sterckx and M. Trigiante,Consistent N=4, D=4 truncation of type IIB supergravity on S1×S5,Phys. Rev. D111(2025) 046019, [2410.23149]. 38

work page arXiv 2025
[2]

Cordaro, P

F. Cordaro, P. Fre, L. Gualtieri, P. Termonia and M. Trigiante,N=8 gaugings revisited: An Exhaustive classification,Nucl. Phys. B532(1998) 245–279, [hep-th/9804056]

work page arXiv 1998
[3]

Nicolai and H

H. Nicolai and H. Samtleben,Maximal gauged supergravity in three-dimensions,Phys. Rev. Lett.86(2001) 1686–1689, [hep-th/0010076]

work page arXiv 2001
[4]

de Wit, H

B. de Wit, H. Samtleben and M. Trigiante,On Lagrangians and gaugings of maximal supergravities,Nucl. Phys. B655(2003) 93–126, [hep-th/0212239]

work page arXiv 2003
[5]

de Wit, H

B. de Wit, H. Samtleben and M. Trigiante,Magnetic charges in local field theory, JHEP09(2005) 016, [hep-th/0507289]

work page arXiv 2005
[6]

de Wit, H

B. de Wit, H. Samtleben and M. Trigiante,The Maximal D=4 supergravities,JHEP06 (2007) 049, [0705.2101]

work page arXiv 2007
[7]

Schon and M

J. Schon and M. Weidner,Gauged N=4 supergravities,JHEP05(2006) 034, [hep-th/0602024]

work page arXiv 2006
[8]

Dall’Agata, N

G. Dall’Agata, N. Liatsos, R. Noris and M. Trigiante,Gauged D = 4N= 4 supergravity,JHEP09(2023) 071, [2305.04015]

work page arXiv 2023
[9]

Lectures on Gauged Supergravity and Flux Compactifications

H. Samtleben,Lectures on Gauged Supergravity and Flux Compactifications,Class. Quant. Grav.25(2008) 214002, [0808.4076]

work page Pith review arXiv 2008
[10]

Trigiante,Gauged Supergravities,Phys

M. Trigiante,Gauged Supergravities,Phys. Rept.680(2017) 1–175, [1609.09745]

work page arXiv 2017
[11]

Inverso and M

G. Inverso and M. Trigiante,New (maximal) gauged supergravities, 3, 2025. 2503.08616

work page arXiv 2025
[12]

Coimbra, C

A. Coimbra, C. Strickland-Constable and D. Waldram,Supergravity as Generalised Geometry I: Type II Theories,JHEP11(2011) 091, [1107.1733]

work page arXiv 2011
[13]

Coimbra, C

A. Coimbra, C. Strickland-Constable and D. Waldram,Supergravity as Generalised Geometry II:E d(d) ×R + and M theory,JHEP03(2014) 019, [1212.1586]

work page arXiv 2014
[14]

Hohm and H

O. Hohm and H. Samtleben,Exceptional Field Theory I:E 6(6) covariant Form of M-Theory and Type IIB,Phys. Rev. D89(2014) 066016, [1312.0614]

work page arXiv 2014
[15]

Hohm and H

O. Hohm and H. Samtleben,Exceptional field theory. II. E 7(7),Phys. Rev. D89(2014) 066017, [1312.4542]

work page arXiv 2014
[16]

Hohm and H

O. Hohm and H. Samtleben,Exceptional field theory. III. E 8(8),Phys. Rev. D90 (2014) 066002, [1406.3348]

work page arXiv 2014
[17]

Aldazabal, D

G. Aldazabal, D. Marques and C. Nunez,Double Field Theory: A Pedagogical Review, Class. Quant. Grav.30(2013) 163001, [1305.1907]

work page arXiv 2013
[18]

Baguet, O

A. Baguet, O. Hohm and H. Samtleben,E 6(6) Exceptional Field Theory: Review and Embedding of Type IIB,PoSCORFU2014(2015) 133, [1506.01065]

work page arXiv 2015
[19]

D. S. Berman and C. D. A. Blair,The Geometry, Branes and Applications of Exceptional Field Theory,Int. J. Mod. Phys. A35(2020) 2030014, [2006.09777]

work page arXiv 2020
[20]

Sterckx,Modave lecture notes: Introduction to Exceptional Field Theory,PoS Modave2023(2025) 004, [2410.19600]

C. Sterckx,Modave lecture notes: Introduction to Exceptional Field Theory,PoS Modave2023(2025) 004, [2410.19600]

work page arXiv 2025
[21]

Samtleben,Exceptional field theories,2503.16947

H. Samtleben,Exceptional field theories,2503.16947

work page arXiv
[22]

Coimbra, C

A. Coimbra, C. Strickland-Constable and D. Waldram,E d(d) ×R + generalised geometry, connections and M theory,JHEP02(2014) 054, [1112.3989]

work page arXiv 2014
[23]

Coimbra, C

A. Coimbra, C. Strickland-Constable and D. Waldram,Supersymmetric Backgrounds and Generalised Special Holonomy,Class. Quant. Grav.33(2016) 125026, [1411.5721]. 39

work page arXiv 2016
[24]

Cassani, G

D. Cassani, G. Josse, M. Petrini and D. Waldram,Systematics of consistent truncations from generalised geometry,JHEP11(2019) 017, [1907.06730]

work page arXiv 2019
[25]

Josse, M

G. Josse, M. Petrini and M. Pico,Consistent Truncations and Generalised Geometry: Scanning through Dimensions and Supersymmetry,2512.03027

work page arXiv
[26]

J. P. Gauntlett and O. Varela,Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions,Phys. Rev. D76(2007) 126007, [0707.2315]

work page arXiv 2007
[27]

Larios and O

G. Larios and O. Varela,MinimalD= 4N= 2supergravity fromD= 11: An M-theory free lunch,JHEP10(2019) 251, [1907.11027]

work page arXiv 2019
[28]

Cassani and P

D. Cassani and P. Koerber,Tri-Sasakian consistent reduction,JHEP01(2012) 086, [1110.5327]

work page arXiv 2012
[29]

Hohm and H

O. Hohm and H. Samtleben,Consistent Kaluza-Klein Truncations via Exceptional Field Theory,JHEP01(2015) 131, [1410.8145]

work page arXiv 2015
[30]

de Wit and H

B. de Wit and H. Nicolai,N=8 Supergravity,Nucl. Phys. B208(1982) 323

1982
[31]

de Wit and H

B. de Wit and H. Nicolai,The Consistency of the S**7 Truncation in D=11 Supergravity,Nucl. Phys. B281(1987) 211–240

1987
[32]

N. P. Warner,Some New Extrema of the Scalar Potential of GaugedN= 8 Supergravity,Phys. Lett. B128(1983) 169–173

1983
[33]

M. J. Duff, B. E. W. Nilsson and C. N. Pope,Kaluza-Klein Supergravity,Phys. Rept. 130(1986) 1–142

1986
[34]

I. M. Comsa, M. Firsching and T. Fischbacher,SO(8) Supergravity and the Magic of Machine Learning,JHEP08(2019) 057, [1906.00207]

work page arXiv 2019
[35]

Inverso,Generalised Scherk-Schwarz reductions from gauged supergravity,JHEP12 (2017) 124, [1708.02589]

G. Inverso,Generalised Scherk-Schwarz reductions from gauged supergravity,JHEP12 (2017) 124, [1708.02589]

work page arXiv 2017
[36]

Inverso and D

G. Inverso and D. Rovere,How to uplift D = 3 maximal supergravities,JHEP02 (2025) 130, [2410.14520]

work page arXiv 2025
[37]

Dall’Agata and G

G. Dall’Agata and G. Inverso,On the Vacua of N = 8 Gauged Supergravity in 4 Dimensions,Nucl. Phys. B859(2012) 70–95, [1112.3345]

work page arXiv 2012
[38]

Gallerati, H

A. Gallerati, H. Samtleben and M. Trigiante,TheN>2supersymmetric AdS vacua in maximal supergravity,JHEP12(2014) 174, [1410.0711]

work page arXiv 2014
[39]

Inverso, H

G. Inverso, H. Samtleben and M. Trigiante,Type II supergravity origin of dyonic gaugings,Phys. Rev. D95(2017) 066020, [1612.05123]

work page arXiv 2017
[40]

Bobev, F

N. Bobev, F. F. Gautason, K. Pilch, M. Suh and J. Van Muiden,Janus and J-fold Solutions from Sasaki-Einstein Manifolds,Phys. Rev. D100(2019) 081901, [1907.11132]

work page arXiv 2019
[41]

Guarino, C

A. Guarino, C. Sterckx and M. Trigiante,N= 2supersymmetric S-folds,JHEP04 (2020) 050, [2002.03692]

work page arXiv 2020
[42]

Giambrone, E

A. Giambrone, E. Malek, H. Samtleben and M. Trigiante,Global properties of the conformal manifold for S-fold backgrounds,JHEP06(2021) 111, [2103.10797]

work page arXiv 2021
[43]

Bobev, F

N. Bobev, F. F. Gautason and J. van Muiden,The holographic conformal manifold of 3dN= 2 S-fold SCFTs,JHEP07(2021) 221, [2104.00977]

work page arXiv 2021
[44]

Giambrone, A

A. Giambrone, A. Guarino, E. Malek, H. Samtleben, C. Sterckx and M. Trigiante, Holographic evidence for nonsupersymmetric conformal manifolds,Phys. Rev. D105 (2022) 066018, [2112.11966]. 40

work page arXiv 2022
[45]

Bobev, F

N. Bobev, F. F. Gautason and J. van Muiden,The conformal manifold of S-folds in string theory,JHEP03(2024) 167, [2312.13370]

work page arXiv 2024
[46]

Guarino, A

A. Guarino, A. Rudra, C. Sterckx and M. Trigiante,Blackening S-folds,JHEP10 (2024) 120, [2407.11593]

work page arXiv 2024
[47]

M. J. Duff and J. T. Liu,Anti-de Sitter black holes in gauged N = 8 supergravity,Nucl. Phys. B554(1999) 237–253, [hep-th/9901149]

work page arXiv 1999
[48]

Cvetic, H

M. Cvetic, H. Lu and C. N. Pope,Four-dimensional N=4, SO(4) gauged supergravity from D = 11,Nucl. Phys. B574(2000) 761–781, [hep-th/9910252]

work page arXiv 2000
[49]

Consistent subsectors of maximal supergravity and wrapped M5-branes

M. Pico and O. Varela,Consistent subsectors of maximal supergravity and wrapped M5-branes,2511.15892

work page internal anchor Pith review Pith/arXiv arXiv
[50]

Ferrero, M

P. Ferrero, M. Inglese, D. Martelli and J. Sparks,Multicharge accelerating black holes and spinning spindles,Phys. Rev. D105(2022) 126001, [2109.14625]

work page arXiv 2022
[51]

Rovere and C

D. Rovere and C. Sterckx,How to uplift non-maximal gauged supergravities, 2510.24850

work page arXiv
[52]

Ferrero, J

P. Ferrero, J. P. Gauntlett, J. M. P. Ipi˜ na, D. Martelli and J. Sparks,Accelerating black holes and spinning spindles,Phys. Rev. D104(2021) 046007, [2012.08530]

work page arXiv 2021
[53]

Cassani, J

D. Cassani, J. P. Gauntlett, D. Martelli and J. Sparks,Thermodynamics of accelerating and supersymmetric AdS4 black holes,Phys. Rev. D104(2021) 086005, [2106.05571]

work page arXiv 2021
[54]

Ferrero, J

P. Ferrero, J. P. Gauntlett and J. Sparks,Supersymmetric spindles,JHEP01(2022) 102, [2112.01543]

work page arXiv 2022
[55]

Couzens, K

C. Couzens, K. Stemerdink and D. van de Heisteeg,M2-branes on discs and multi-charged spindles,JHEP04(2022) 107, [2110.00571]

work page arXiv 2022
[56]

Ferrero, J

P. Ferrero, J. P. Gauntlett, D. Martelli and J. Sparks,M5-branes wrapped on a spindle, JHEP11(2021) 002, [2105.13344]

work page arXiv 2021
[57]

Bomans and C

P. Bomans and C. Couzens,On the classSorigin of spindle solutions,JHEP10(2024) 036, [2404.08083]

work page arXiv 2024
[58]

Louis and H

J. Louis and H. Triendl,Maximally supersymmetric AdS 4 vacua in N = 4 supergravity, JHEP10(2014) 007, [1406.3363]

work page arXiv 2014
[59]

Guarino and C

A. Guarino and C. Sterckx,S-folds and holographic RG flows on the D3-brane,JHEP 06(2021) 051, [2103.12652]

work page arXiv 2021
[60]

I. Arav, J. P. Gauntlett, M. M. Roberts and C. Rosen,Marginal deformations and RG flows for type IIB S-folds,JHEP07(2021) 151, [2103.15201]

work page arXiv 2021
[61]

Guarino and C

A. Guarino and C. Sterckx,Flat deformations of type IIB S-folds,JHEP11(2021) 171, [2109.06032]

work page arXiv 2021
[62]

Ces` aro, G

M. Ces` aro, G. Larios and O. Varela,The spectrum of marginally-deformedN= 2 CFTs with AdS 4 S-fold duals of type IIB,JHEP12(2021) 214, [2109.11608]

work page arXiv 2021
[63]

Guarino and C

A. Guarino and C. Sterckx,Type IIB S-folds: flat deformations, holography and stability,PoSCORFU2021(2022) 163, [2204.09993]

work page arXiv 2022
[64]

Group actions on manifolds

E. Meinrenken, “Group actions on manifolds.” https://www.math.toronto.edu/mein/teaching/LectureNotes/action.pdf, 2003

2003
[65]

Andrianopoli, R

L. Andrianopoli, R. D’Auria, S. Ferrara, P. Fre and M. Trigiante,E(7)(7) duality, BPS black hole evolution and fixed scalars,Nucl. Phys. B509(1998) 463–518, [hep-th/9707087]. 41

work page arXiv 1998
[66]

Assel and A

B. Assel and A. Tomasiello,Holographic duals of 3d S-fold CFTs,JHEP06(2018) 019, [1804.06419]

work page arXiv 2018
[67]

S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory,

D. Gaiotto and E. Witten,S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory,Adv. Theor. Math. Phys.13(2009) 721–896, [0807.3720]

work page arXiv 2009
[68]

Microstates of Accelerating and Supersymmetric AdS4 Black Holes from the Spindle Index

E. Colombo, S. M. Hosseini, D. Martelli, A. Pittelli and A. Zaffaroni,Microstates of Accelerating and Supersymmetric AdS4 Black Holes from the Spindle Index,Phys. Rev. Lett.133(2024) 031603, [2404.07173]

work page arXiv 2024
[69]

Coccia and C

L. Coccia and C. F. Uhlemann,On the planar limit of 3dT σ ρ [SU (N)],JHEP06(2021) 038, [2011.10050]

work page arXiv 2021
[70]

Anabalon and S.F

A. Anabalon and S. F. Ross,Supersymmetric solitons and a degeneracy of solutions in AdS/CFT,JHEP07(2021) 015, [2104.14572]

work page arXiv 2021
[71]

U-Duality and Central Charges in Various Dimensions Revisited

L. Andrianopoli, R. D’Auria and S. Ferrara,U duality and central charges in various dimensions revisited,Int. J. Mod. Phys. A13(1998) 431–490, [hep-th/9612105]

work page Pith review arXiv 1998
[72]

Sezgin,Survey of supergravities,2312.06754

E. Sezgin,Survey of supergravities,2312.06754

work page arXiv
[73]

P. K. Townsend,Cosmological Constant in Supergravity,Phys. Rev. D15(1977) 2802–2804

1977
[74]

Sparks,Sasaki-Einstein Manifolds,Surveys Diff

J. Sparks,Sasaki-Einstein Manifolds,Surveys Diff. Geom.16(2011) 265–324, [1004.2461]. 42

work page arXiv 2011