arXiv subjects

Camille Eloy

Publications and source records attributed to Camille Eloy.

12 recordsLinked to original sources

arXiv2026

Kaluza-Klein Perturbation Theory from Exceptional Field Theory

We develop the perturbation theory of ten and eleven-dimensional supergravities on a large class of Kaluza-Klein backgrounds including familiar AdS examples such as AdS$_5\times S^5$, but also more general manifolds such as black hole geometries. Employing ${\rm E}_{6(6)}$ exceptional field theory with the backgrounds characterized by a generalized Scherk-Schwarz ansatz, we determine the first order field equations for the fluctuations that are gauge invariant under linearized generalized diffeomorphisms. We then present the details of the Higgs mechanism for all fields including spin-2 for the subset of backgrounds in which higher-form gauge fields vanish. We use a recently established machinery based on homotopy transfer that allows one to separate the fields into gauge invariant physical modes and pure gauge unphysical modes to all orders in perturbation theory. Finally, as a first application for backgrounds with higher-form gauge fields switched on, we analyze part of the spectrum of ten-dimensional Kaluza-Klein modes of type IIB supergravity around a Kerr-Newman AdS$_5$ black hole that in the near horizon limit becomes a fibered product of AdS$_2$ and a squashed three-sphere.

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arXiv2026

Homotopy transfer for massive Kaluza-Klein modes

We develop techniques to treat massive Kaluza-Klein modes to arbitrary order in perturbation theory. The Higgs mechanism that renders the higher Kaluza-Klein modes massive is displayed. To this end we give an algorithm in perturbation theory that yields new fields with the following characteristics: they are gauge invariant under all higher-mode gauge transformations, which are broken, but they transform covariantly under the zero-mode gauge transformations, which are unbroken. We employ the formulation of field theory in terms of $L_{\infty}$ algebras together with their homotopy transfer, which here maps the gauge redundant fields of gravity to gauge invariant fields. We illustrate these results, as a proof of concept, for Kaluza-Klein theory on a torus. In an accompanying paper these results will be applied to a large class of generalized Scherk-Schwarz backgrounds in exceptional field theory.

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arXiv2025

Machine Learning the Conformal Manifold of Holographic CFT$_{2}$s

We investigate the structure of conformal manifolds around AdS$_3 \times S^3$ which lift from continuous flat directions in the scalar potential of gauged supergravity resulting from six-dimensional $\mathcal{N}=(1,1)$ supergravity. Our approach combines numerical exploration and symbolic inference. For the latter, we develop a symbolic regression algorithm based on Annealed Sequential Monte Carlo samplers, a combination of Annealed Importance Sampling and Sequential Monte Carlo samplers, well-suited to uncovering polynomial constraints in high-dimensional parameter spaces. The algorithm reconstructs a set of polynomial relations that provides an explicit analytic parametrization of a new family of solutions.

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arXiv2024

Charting the Conformal Manifold of Holographic CFT$_2$'s

We construct new continuous families of ${\rm AdS}_3\times S^3\times {\rm T}^4$ and ${\rm AdS}_3\times S^3\times S^3\times S^1$ solutions in heterotic and type II supergravities. These families are found in three-dimensional consistent truncations and controlled by 17 parameters, which include TsT $β$ deformations and encompass several supersymmetric sub-families. The different uplifts are constructed in a unified fashion by means of Exceptional Field Theory (ExFT). This allows the computation of the Kaluza-Klein spectra around the deformations, to test the stability of the solutions, and to interpret them holographically and as worldsheet models. To achieve this, we describe how the half-maximal ${\rm SO}(8,8)$ ExFT can be embedded into ${\rm E}_{8(8)}$ ExFT.

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arXiv2023

On non-supersymmetric stable marginal deformations in AdS$_3$/CFT$_2$

We discuss a continuous family of non-supersymmetric AdS$_3\times S^3\times{\rm T^4}$ vacua in heterotic and type II supergravities whose complete Kaluza-Klein spectrum is computed and found to be free from instabilities. This family is protected as well against some non-perturbative decay channels, and as such it provides the first candidate for a non-supersymmetric holographic conformal manifold in 2$d$. We also describe the operators realising the deformations in the worldsheet and boundary CFT's.

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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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arXiv2022

U-duality and $α'$ corrections in three dimensions

We consider the target space theory of bosonic and heterotic string theory to first order in $α'$ compactified to three dimensions, using a formulation that is manifestly T-duality invariant under ${\rm O}(d,d,\mathbb{R})$ with $d=23$ and $d=7$, respectively. While the two-derivative supergravity exhibits a symmetry enhancement to the U-duality group ${\rm O}(d+1,d+1)$, the continuous group is known to be broken to ${\rm O}(d,d,\mathbb{R})$ by the first $α'$ correction. We revisit this observation by computing the full effective actions in three dimensions to first order in $α'$ by dualizing the vector gauge fields. We give a formally ${\rm O}(d+1,d+1)$ invariant formulation by invoking a vector compensator, and we observe a chiral pattern that allows one to reconstruct the bosonic action from the heterotic action. Furthermore, we obtain a particular massive deformation by integrating out the external $B$ field. This induces a novel Chern-Simons term based on composite connections that, remarkably, is ${\rm O}(d+1,d+1)$ invariant to leading order in the deformation parameter.

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arXiv2022

Triality and the consistent reductions on ${\rm AdS}_3\times S^3$

We study compactifications on ${\rm AdS}_3\times S^3$ and deformations thereof. We exploit the triality symmetry of the underlying duality group ${\rm SO}(4,4)$ of three-dimensional supergravity in order to construct and relate new consistent truncations. For non-chiral $D=6$, ${\cal N}_{\rm 6d}=(1,1)$ supergravity, we find two different consistent truncations to three-dimensional supergravity, retaining different subsets of Kaluza-Klein modes, thereby offering access to different subsectors of the full nonlinear dynamics. As an application, we construct a two-parameter family of ${\rm AdS}_3\times M^3$ backgrounds on squashed spheres preserving ${\rm U}(1)^2$ isometries. For generic value of the parameters, these solutions break all supersymmetries, yet they remain perturbatively stable within a non-vanishing region in parameter space. They also contain a one-parameter family of ${\cal N}=(0,4)$ supersymmetric ${\rm AdS}_3\times M^3$ backgrounds on squashed spheres with ${\rm U}(2)$ isometries. Using techniques from exceptional field theory, we determine the full Kaluza-Klein spectrum around these backgrounds.

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arXiv2021

Kaluza-Klein spectrometry for ${\rm AdS_{3}}$ vacua

We use exceptional field theory to compute Kaluza-Klein mass spectra around ${\rm AdS_{3}}$ vacua that sit in half-maximal gauged supergravity in three dimensions. The formalism applies to any vacuum that arises from a consistent truncation of higher-dimensional supergravity, no matter what symmetries are preserved. We illustrate its efficiency by computing the spectra of ${\cal N}=(2,0)$ and ${\cal N}=(1,1)$ six-dimensional supergravities on ${\rm AdS_{3}}\times S^{3}$ and of type II supergravity on ${\rm AdS_{3}}\times S^{3}\times S^{3}\times S^{1}$.

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arXiv2020

Duality Invariance and Higher Derivatives

We dimensionally reduce the spacetime action of bosonic string theory, and that of the bosonic sector of heterotic string theory after truncating the Yang-Mills gauge fields, on a $d$-dimensional torus including all higher-derivative corrections to first order in $α'$. A systematic procedure is developed that brings this action into a minimal form in which all fields except the metric carry only first order derivatives. This action is shown to be invariant under ${\rm O}(d,d,\mathbb{R})$ transformations that acquire $α'$-corrections through a Green-Schwarz type mechanism. We prove that, up to a global pre-factor, the first order $α'$-corrections are uniquely determined by ${\rm O}(d,d,\mathbb{R})$ invariance.

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arXiv2020

Green-Schwarz Mechanism for String Dualities

We determine the complete spacetime action to first order in $α'$ for the massless fields of bosonic string theory compactified on a $d$-dimensional torus. A fully systematic procedure is developed that brings the action into a minimal form in which all fields apart from the metric enter only with first-order derivatives. T-duality implies that this action must have a global $\mathrm{O}(d,d,\mathbb{R})$ symmetry, and we show that this requires a Green-Schwarz type mechanism for $α'$-deformed $\mathrm{O}(d,d,\mathbb{R})$ transformations. In terms of a frame formalism with ${\rm GL}(d)\times {\rm GL}(d)$ gauge symmetry this amounts to a modification of the three-form curvature by a Chern-Simons term for composite gauge fields.

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arXiv2019

${\mathcal{N}=(8,0)}$ AdS vacua of three-dimensional supergravity

We give a classification of fully supersymmetric chiral ${\cal N}=(8,0)$ AdS$_3$ vacua in general three-dimensional half-maximal gauged supergravities coupled to matter. These theories exhibit a wealth of supersymmetric vacua with background isometries given by the supergroups OSp$(8|2,\mathbb{R})$, F(4), SU$(4|1,1)$, and OSp$(4^*|4)$, respectively. We identify the associated embedding tensors and the structure of the associated gauge groups. We furthermore compute the mass spectra around these vacua. As an off-spin we include results for a number of ${\cal N}=(7,0)$ vacua with supergroups OSp$(7|2,\mathbb{R})$ and G$(3)$, respectively. We also comment on their possible higher-dimensional uplifts.

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