arXiv subjects

Emanuel Malek

Publications and source records attributed to Emanuel Malek.

At least 19 recordsLinked to original sources

arXiv2024

Consistent truncations and G$_2$-invariant AdS$_4$ solutions of $D=11$ supergravity

Maximal supergravities in ten and eleven dimensions admit consistent truncations on particular spheres to maximal supergravities in lower dimensions. Concurrently, the truncation to singlets under any subgroup of the sphere isometry group leads to consistent truncations with less or no supersymmetry. We review the relation between these truncations in the framework of exceptional field theory. As an application, we derive three new G$_2$-invariant solutions of $D=11$ supergravity. Their geometry is of the form AdS$_4\times Σ_7$ where $Σ_7$ is a deformed seven-sphere, preserving SO(7) isometries.

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arXiv2024

Y-algebroids and $E_{7(7)} \times \mathbb{R}^+$-generalised geometry

We define the notion of Y-algebroids, generalising the Lie, Courant, and exceptional algebroids that have been used to capture the local symmetry structure of type II string theory and M-theory compactifications to $D \geq 5$ dimensions. Instead of an invariant inner product, or its generalisation arising in exceptional algebroids, Y-algebroids are built around a specific type of tensor, denoted $Y$, that provides exactly the necessary properties to also describe compactifications to $D=4$ dimensions. We classify "M-exact" $E_7$-algebroids and show that this precisely matches the form of the generalised tangent space of $E_{7(7)} \times \mathbb{R}^+$-generalised geometry, with possible twists due to 1-, 4- and 7-form fluxes, corresponding physically to the derivative of the warp factor and the M-theory fluxes. We translate the notion of generalised Leibniz parallelisable spaces, relevant to consistent truncations, into this language, where they are mapped to so-called exceptional Manin pairs. We also show how to understand Poisson-Lie U-duality and exceptional complex structures using Y-algebroids.

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arXiv2023

Cubic and higher-order supergravity couplings for AdS vacua using Exceptional Field Theory

We show how to use Exceptional Field Theory to efficiently compute $n$-point couplings of all Kaluza-Klein modes for vacua that can be uplifted from maximal gauged supergravities to 10/11 dimensions via a consistent truncation. Via the AdS/CFT correspondence, these couplings encode the $n$-point functions of holographic conformal fields theories. Our methods show that these $n$-point couplings are controlled by the $n$-point invariant of scalar harmonics of the maximally symmetric point of the truncation, allowing us to show that infinitely-many $n$-point couplings vanish for any vacua of the truncation, even though they may be allowed by the remnant symmetry group of the vacua. This gives new results even for the maximally supersymmetric AdS$_5 \times S^5$, AdS$_4 \times S^7$ and AdS$_7 \times S^4$ vacua of string and M-theory, where we prove old conjectures about the vanishing of $n$-point extremal and near-extremal couplings. Focusing in particular on cubic couplings for vacua of 5-dimensional gauged supergravity, we derive explicit universal formulae encoding these couplings for any vacuum within a consistent truncation. We use this to compute known and new couplings involving spin-0, spin-1, spin-2 for the AdS$_5 \times S^5$ vacuum of IIB string theory.

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arXiv2023

Adding fluxes to consistent truncations: IIB supergravity on ${\rm AdS}_3 \times S^3 \times S^3 \times S^1$

We use $E_{8(8)}$ Exceptional Field Theory to construct the consistent truncation of IIB supergravity on $S^3 \times S^3 \times S^1$ to maximal 3-dimensional ${\cal N}=16$ gauged supergravity containing the ${\cal N}=(4,4)$ AdS$_3$ vacuum. We explain how to achieve this by adding a 7-form flux to the $S^1$ reduction of the dyonic $E_{7(7)}$ truncation on $S^3 \times S^3$ previously constructed in the literature. Our truncation Ansatz includes, in addition to the ${\cal N}=(4,4)$ vacuum, a host of moduli breaking some or all of the supersymmetries. We explicitly construct the uplift of a subset of these to construct new supersymmetric and non-supersymmetric AdS$_3$ vacua of IIB string theory, which include a range of perturbatively stable non-supersymmetric 10-d vacua. Moreover, we show how the supersymmetric direction of the moduli space of AdS$_3$ vacua of six-dimensional gauged supergravity studied in arXiv:2111.01167 is compactified upon lifting to 10 dimensions, and find evidence of T-duality playing a role in global aspects of the moduli space. Along the way, we also derive the form of 3-dimensional ${\cal N}=16$ gauged supergravity in terms of the embedding tensor and rule out a 10-/11-dimensional origin of some 3-dimensional gauged supergravities.

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arXiv2023

A holographic RG flow from the squashed to the round $S^7$

We construct and analyze the domain wall solution in $D=11$ supergravity connecting the $N=1$, AdS$_4\times S_{\rm squashed}^7$ vacuum to the $N=8$, AdS$_4\times S_{\rm round}^7$ vacuum. This domain wall describes the holographic renormalization group flow from an ${\rm Sp}(2)\times {\rm Sp}(1)$ symmetric UV fixed point to the ${\rm SO}(8)$ symmetric IR fixed point. It breaks all supersymmetries which are (partially) restored at its endpoints. We show how recent techniques from exceptional field theory allow us to compute the quadratic couplings of all Kaluza-Klein fluctuations around the domain wall background, encoding all two-point correlators along the holographic RG flow.

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arXiv2023

Holographic Evidence for Non-Supersymmetric Conformal Manifolds

We provide the first holographic evidence for the existence of a non-supersymmetric conformal manifold arising from exactly marginal but supersymmetry-breaking deformations of a superconformal three-dimensional field theory. In particular, we construct a 2-parameter non-supersymmetric deformation of a supersymmetric AdS non-geometric background in Type IIB string theory. We prove that the non-supersymmetric backgrounds are perturbatively stable and also do not suffer from various non-perturbative instabilities. Finally, we argue that diffeomorphism symmetry protects our solutions against higher-derivative string corrections.

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arXiv2023

Kaluza-Klein Spectrometry beyond Consistent Truncations: The Squashed $S^7$

We show how to use Exceptional Field Theory to compute the full Kaluza-Klein spectra of 10- and 11-dimensional supergravity around deformations of backgrounds of maximal gauged supergravity by scalar modes that do not form part of the consistent truncation. This includes deformations of AdS$_4 \times S^7$ and AdS$_5 \times S^5$ by modes that are not part of the ${\cal N}=8$ supermultiplet. As an application, we compute the full Kaluza-Klein spectrum of the ${\cal N}=1$ and ${\cal N}=0$ squashed $S^7$. In this example, all conformal dimensions are captured by a universal formula in terms of the Casimir operators and additional quantum numbers which organise the spectrum.

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arXiv2022

Consistent truncations to 3-dimensional supergravity

We show how to construct consistent truncations of 10-/11-dimensional supergravity to 3-dimensional gauged supergravity, preserving various amounts of supersymmetry. We show, that as in higher dimensions, consistent truncations can be defined in terms of generalised $G$-structures in Exceptional Field Theory, with $G \subset E_{8(8)}$ for the 3-dimensional case. Differently from higher dimensions, the generalised Lie derivative of $E_{8(8)}$ Exceptional Field Theory requires a set of "covariantly constrained" fields to be well-defined, and we show how these can be constructed from the $G$-structure itself. We prove several general features of consistent truncations, allowing us to rule out a higher-dimensional origin of many 3-dimensional gauged supergravities. In particular, we show that the compact part of the gauge group can be at most $\mathrm{SO}(9)$ and that there are no consistent truncations on a 7-or 8-dimensional product of spheres such that the full isometry group of the spheres is gauged. Moreover, we classify which matter-coupled ${\cal N} \geq 4$ gauged supergravities can arise from consistent truncations. Finally, we give several examples of consistent truncations to three dimensions. These include the truncations of IIA and IIB supergravity on $S^7$ leading to two different ${\cal N}=16$ gauged supergravites, as well as more general IIA/IIB truncations on $H^{p,7-p}$. We also show how to construct consistent truncations on compactifications of IIB supergravity on $S^5$ fibred over a Riemann surface. These result in 3-dimensional ${\cal N}=4$ gauged supergravities with scalar manifold ${\cal M} = \frac{\mathrm{SO}(6,4)}{\mathrm{SO}(6) \times \mathrm{SO}(4)} \times \frac{\mathrm{SU}(2,1)}{\mathrm{S}(\mathrm{U}(2)\times\mathrm{U}(1))}$ with a $\mathrm{ISO}(3)\times\mathrm{U}(1)^4$ gauging and for hyperboloidal Riemann surfaces contain ${\cal N}=(2,2)$ AdS$_3$ vacua.

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arXiv2022

Romans massive QP manifolds

We introduce QP manifolds that capture the generalised geometry of type IIA string backgrounds with Ramond-Ramond fluxes and Romans mass. Each of these is associated to a BPS brane in type IIA: a D2, D4, or NS5-brane. We explain how these probe branes are related to their associated QP-manifolds via the AKSZ topological field theory construction and the recent brane phase space construction. M-theory/type IIA duality is realised on the QP-manifold side as symplectic reduction along the M-theory circle (for branes that do not wrap it); this always produces IIA QP-manifolds with vanishing Romans mass.

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arXiv2021

The higher-dimensional origin of five-dimensional $\boldsymbol{{\cal N}\!=\!2}$ gauged supergravities

Using exceptional generalised geometry, we classify which five-dimensional ${\cal N}=2$ gauged supergravities can arise as a consistent truncation of 10-/11-dimensional supergravity. Exceptional generalised geometry turns the classification into an algebraic problem of finding subgroups $G_S \subset \mathrm{USp}(8) \subset \mathrm{E}_{6(6)}$ that preserve exactly two spinors. Moreover, the intrinsic torsion of the $G_S$ structure must contain only constant singlets under $G_S$, and these, in turn, determine the gauging of the five-dimensional theory. The resulting five-dimensional theories are strongly constrained: their scalar manifolds are necessarily symmetric spaces and only a small number of matter multiplets can be kept, which we completely enumerate. We also determine the largest reductive and compact gaugings that can arise from consistent truncations.

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arXiv2021

Global Properties of the Conformal Manifold for S-Fold Backgrounds

We study a one-parameter family of $\mathcal{N}=2$ anti-de Sitter vacua with ${\rm U}(1)^2$ symmetry of gauged four-dimensional maximal supergravity, with dyonic gauge group $[{\rm SO}(6)\times {\rm SO}(1,1)]\ltimes \mathbb{R}^{12}$. These backgrounds are known to correspond to Type IIB S-fold solutions with internal manifold of topology $S^1\times S^5$. The family of AdS$_4$ vacua is parametrized by a modulus $χ$. Although $χ$ appears non-compact in the four-dimensional supergravity, we show that this is just an artefact of the four-dimensional description. We give the 10-dimensional geometric interpretation of the modulus and show that it actually has periodicity of $\frac{2π}{T}$, which is the inverse radius of $S^1$. We deduce this by providing the explicit $D=10$ uplift of the family of vacua as well as computing the entire modulus-dependent Kaluza-Klein spectrum as a function of $χ$. At the special values $χ=0$ and $χ=\fracπ{T}$, the symmetry enhances according to ${\rm U}(1)^2\rightarrow{\rm U}(2)$, giving rise however to inequivalent Kaluza-Klein spectra. At $χ=\fracπ{T}$, this realizes a bosonic version of the "space invaders" scenario with additional massless vector fields arising from formerly massive fields at higher Kaluza-Klein levels.

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arXiv2021

Kaluza-Klein Spectroscopy for the Leigh-Strassler SCFT

We apply recently developed tools from exceptional field theory to calculate the full Kaluza-Klein spectrum of the AdS$_5$ Pilch-Warner solution of type IIB supergravity. Through the AdS/CFT correspondence this yields detailed information about the spectrum of protected and unprotected operators of the four-dimensional $\mathcal{N}=1$ Leigh-Strassler SCFT, in the planar limit. We also calculate explicitly the superconformal index of the SCFT in this limit and show that it agrees precisely with the spectrum of protected operators in the supergravity calculation.

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arXiv2021

Stable non-supersymmetric Anti-de Sitter vacua of massive IIA supergravity

Stable non-supersymmetric Anti-de Sitter (AdS) vacua of string theory are widely believed not to exist. In this letter, we analytically compute the full bosonic Kaluza-Klein spectrum around the ${\rm G_2}$-invariant non-supersymmetric $\textrm{AdS}_4$ solution of massive IIA supergravity, and show that it is perturbatively stable. We also provide evidence that six other non-supersymmetric $\textrm{AdS}_4$ solutions of massive IIA supergravity are perturbatively stable. Since previous studies have indicated that these AdS vacua may also be non-perturbatively stable, our findings pose a challenge to the Swampland Conjecture.

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arXiv2020

Consistent truncations around half-maximal AdS$_5$ vacua of 11-dimensional supergravity

We use exceptional field theory to systematically study all possible consistent truncations around half-maximal AdS$_5$ vacua of M-theory. We show that only truncations with at most three vector multiplets are consistent. The possible gaugings are SU(2)$\times$U(1) and ISO(3)$\times$U(1) where, in the first case, the U(1) factor can have different embeddings inside the global symmetry group SO$(5,n)$, where $n \leq 3$ equals the number of vector multiplets. We show that the ISO(3)$\times$U(1) truncation only exists around vacua that are locally an $S^4$ fibration over a Riemann surface, and argue that this is the only consistent truncation with vector multiplets around these vacua that can be constructed by going through the 7-dimensional SO(5) gauged supergravity obtained after an $S^4$ reduction. The consistent truncations with SU(2)$\times$U(1) gaugings with vector multiplets exist only if certain conditions are satisfied, which we derive.

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arXiv2020

Kaluza-Klein Spectrometry from Exceptional Field Theory

Exceptional field theories yield duality-covariant formulations of higher-dimensional supergravity. They have proven to be an efficient tool for the construction of consistent truncations around various background geometries. In this paper, we demonstrate how the formalism can moreover be turned into a powerful tool for computing the Kaluza-Klein mass spectra around these backgrounds. Most of these geometries have little to no remaining symmetries and their spectra are accessible to standard methods only in selected subsectors. The present formalism not only grants access to the full Kaluza-Klein spectra but also provides the scheme to identify the resulting mass eigenstates in higher dimensions. As a first illustration, we rederive in compact form the mass spectrum of IIB supergravity on $S^5$. We further discuss the application of our formalism to determine the mass spectra of higher Kaluza-Klein multiplets around the warped geometries corresponding to some prominent ${\cal N}=2$ and ${\cal N}=0$ AdS vacua in maximal supergravity.

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arXiv2020

Tachyonic Kaluza-Klein modes and the AdS swampland conjecture

We compute the Kaluza-Klein spectrum of the non-supersymmetric SO(3)$\,\times\,$SO(3)-invariant AdS$_4$ vacuum of 11-dimensional supergravity, whose lowest-lying Kaluza-Klein modes belong to a consistent truncation to 4-dimensional ${\cal N}=8$ supergravity and are stable. We show that, nonetheless, the higher Kaluza-Klein modes become tachyonic so that this non-supersymmetric AdS$_4$ vacuum is perturbatively unstable within 11-dimensional supergravity. This represents the first example of unstable higher Kaluza-Klein modes and provides further evidence for the AdS swampland conjecture, which states that there are no stable non-supersymmetric AdS vacua within string theory. We also find 27 infinitesimal moduli amongst the Kaluza-Klein modes, which hints at the existence of a family of non-supersymmetric AdS$_4$ vacua.

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arXiv2020

E$_{6(6)}$ Exceptional Drinfel'd Algebras

The exceptional Drinfel'd algebra (EDA) is a Leibniz algebra introduced to provide an algebraic underpinning with which to explore generalised notions of U-duality in M-theory. In essence it provides an M-theoretic analogue of the way a Drinfel'd double encodes generalised T-dualities of strings. In this note we detail the construction of the EDA in the case where the regular U-duality group is $E_{6(6)}$. We show how the EDA can be realised geometrically as a generalised Leibniz parallelisation of the exceptional generalised tangent bundle for a six-dimensional group manifold $G$, endowed with a Nambu-Lie structure. When the EDA is of coboundary type, we show how a natural generalisation of the classical Yang-Baxter equation arises. The construction is illustrated with a selection of examples including some which embed Drinfel'd doubles and others that are not of this type.

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arXiv2020

Open-String Non-Associativity in an R-flux Background

We derive the commutation relations for open-string coordinates on D-branes in non-geometric background spaces. Starting from D0-branes on a three-dimensional torus with H-flux, we show that open strings with end points on D3-branes in a three-dimensional R-flux background exhibit a non-associative phase-space algebra, which is similar to the non-associative R-flux algebra of closed strings. Therefore, the effective open-string gauge theory on the D3-branes is expected to be a non-associative gauge theory. We also point out differences between the non-associative phase space structure of open and closed strings in non-geometric backgrounds, which are related to the different structure of the world-sheet commutators of open and closed strings.

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