Eleven-dimensional Supergravity Research Articles

New asymptotically (anti)-de Sitter black holes in (super)gravity

We use the duality between gravitational dynamics and fluids living on dynamical surfaces carrying multiple charges, known as the blackfold approach, to perturbatively construct new asymptotically global (Anti)-de Sitter multi-spinning, non-extremal, multi-charged black holes in theories of higher-dimensional gravity minimally coupled to a dilaton and higher-form gauge fields in spacetime dimensions D ≥ 5, and new asymptotically AdSl × Sm black holes in type IIB and eleven-dimensional supergravity. These solutions include the generalisation of the Kerr-Newman solution to (A)dS carrying either electric or string charge, generalisations of black rings to higher-dimensions with \U0001d54ap × \U0001d54an+1 horizon topology, static de Sitter solutions carrying arbitrary q-brane charge, as well as various asymptotically AdSl× Sm multi-charged and multi-spinning black hole solutions, some of which correspond to novel thermal states in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 Super-Yang-Mills theory.

Non-relativistic M2-branes and the AdS/CFT correspondence

A non-relativistic limit of the AdS/CFT correspondence is studied in the context of M2-branes. On the field theory side this corresponds to a near-BPS limit of ABJM that localises onto solutions of Hitchin’s equations. It is shown that the symmetries of the theory include an infinite-dimensional enhancement of the spatial symmetry algebra corresponding to time-dependent holomorphic transformations. Taking the limit of the gravitational dual splits the geometry into three ‘large’ directions and eight ‘small’ directions and corresponds to the Membrane-Newton-Cartan limit of eleven-dimensional supergravity. This has the effect of reducing the AdS4 factor to an AdS2 factor for the near-horizon limit of the M2-brane metric. Evidence is presented that the duality is maintained after the limit.

M5-branes and D4-branes wrapped on a direct product of spindle and Riemann surface

We construct multi-charged AdS3× ⅀ ×Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document} and AdS2× ⅀ ×Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document} solutions from M5-branes and D4-branes wrapped on a direct product of spindle, ⅀, and Riemann surface, Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document}. Employing uplift formula, we obtain these solutions by uplifting the multi-charged AdS3× ⅀ and AdS2× ⅀ solutions to seven and six dimensions, respectively. We further uplift the solutions to eleven-dimensional and massive type IIA supergravity and calculate the holographic central charge and the Bekenstein-Hawking entropy, respectively. We perform the gravitational block calculations and, for the AdS3× ⅀ ×Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document} solutions, the result precisely matches the holographic central charge from the supergravity solutions.

The complete Kaluza-Klein spectra of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 and N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 0 M-theory on AdS4× (squashed S7)

The squashed seven-sphere operator spectrum is completed by deriving the spectrum of the spin-3/2 operator. The implications of the results for the AdS4N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supermultiplets obtained from compactification of eleven-dimensional supergravity are analysed. The weak G2 holonomy plays an important role when solving the eigenvalue equations on the squashed sphere. Here, a novel and more universal algebraic approach to the whole eigenvalue problem on coset manifolds is provided. Having obtained full control of all the operator spectra, we can finally determine the irreps D(E0, s) for all supermultiplets in the left-squashed vacuum. This includes an analysis of possible boundary conditions. By performing an orientation flip on the seven-sphere, we also obtain the full spectrum for the non-supersymmetric right-squashed compactification which is of interest in the swampland context and in particular for the AdS swampland conjecture. Here, a number of boundary condition ambiguities arise making the analysis of dual marginal operators somewhat involved. This work is a direct continuation of [1] and [2].

De-Higgsing in eleven-dimensional supergravity on the squashed S 7

Abstract In this paper we construct the subset of modes on S 7 that are relevant in the compactification of eleven-dimensional supergravity on a squashed S 7 when restricted to the sector that comprises singlets under the S p ( 1 ) × S p ( 2 ) isometry of the squashed sphere. Some of the properties of these modes, connected to the transition from the round S 7 to the squashed S 7, are analysed in detail. Special features of the Rarita–Schwinger operator, described in earlier work by Buchdahl, are explained and related to properties of the squashed S 7 operator spectrum obtained in previous work by the authors. We then discuss how the singlet modes give rise to supermultiplets in the left-squashed case, the phenomenon of de-Higgsing, and what happens to the AdS4 fields in these supermultiplets under an orientation reversal (‘skew-whiffing’) of the squashed S 7. Finally, we consider the possible choices of boundary conditions that appear for some of these fields in AdS4 in the case of the right-squashed non-supersymmetric compactification, and how these choices may affect the stability of the gravity theory.

Consistent truncation of eleven-dimensional supergravity on S8× S1

Eleven-dimensional supergravity on S8 × S1 is conjectured to be dual to the M-theory matrix model. We prove that the dynamics of a subset of fluctuations around this background is consistently described by D = 2 SO(9) gauged maximal supergravity. We provide the full non-linear uplift formulæ for all bosonic fields. We also present a further truncation to the SO(3)×SO(6) invariant sector and discuss its relation to the BMN matrix model at finite temperature. The construction relies on the framework of generalised Scherk-Schwarz reductions, established for E9 exceptional field theory in a companion paper. As a by-product, we severely constrain the most general gauge deformations in D = 2 admitting an uplift to higher dimensions.

Towards AdS distances in string theory

The AdS Distance Conjecture proposes to assign a notion of distance between AdS vacua in quantum gravity. We perform some initial developments of this idea. We first propose more sharply how to define a metric on conformal variations of AdS through the action. This metric is negative, making the distance ill-defined, a property relating to the famous conformal factor problem of quantum gravity. However, in string theory, variations of the AdS conformal factor are accompanied by variations of the internal dimensions and of the background flux. We propose an action metric, which accounts for all of these variations simultaneously. Accounting for the variations of the overall volume of the internal dimensions can flip the sign of the action metric making it positive. This positivity is related to the absence of scale separation between the internal and external dimensions: the negative external conformal contribution must be sub-dominant to the positive internal contribution. We then focus specifically on the families of solutions of eleven-dimensional supergravity on AdS4 × S7 and AdS7 × S4. For these, there is only a single further additional contribution to the action metric coming from variations of the Freund-Rubin flux. This contribution is subtle to implement, and the unique prescription we find requires singling out the radial direction of AdS as special. Adding the flux contribution yields an overall total action metric which becomes positive for both the AdS4 and AdS7 families of solutions. The final result is therefore a procedure which yields a well-defined distance for these families of solutions.

Decomposable (5, 6)-solutions in eleven-dimensional supergravity

We present decomposable (5, 6)-solutions M̃1,4×M6 in eleven-dimensional supergravity by solving the bosonic supergravity equations for a variety of non-trivial flux forms. Many of the bosonic backgrounds presented here are induced by various types of null flux forms on products of certain totally Ricci-isotropic Lorentzian Walker manifolds and Ricci-flat Riemannian manifolds. These constructions provide an analogy of the work performed by Chrysikos and Galaev [Classical Quantum Gravity 37, 125004 (2020)], who made similar computations for decomposable (6, 5)-solutions. We also present bosonic backgrounds that are products of Lorentzian Einstein manifolds with a negative Einstein constant (in the “mostly plus” convention) and Riemannian Kähler–Einstein manifolds with a positive Einstein constant. This conclusion generalizes a result of Pope and van Nieuwenhuizen [Commun. Math. Phys. 122, 281–292 (1989)] concerning the appearance of six-dimensional Kähler–Einstein manifolds in eleven-dimensional supergravity. In this setting, we construct infinitely many non-symmetric decomposable (5, 6)-supergravity backgrounds by using the infinitely many Lorentzian Einstein–Sasakian structures with a negative Einstein constant on the 5-sphere, known from the work of Boyer et al. [Commun. Math. Phys. 262, 177–208 (2006)].

N = (2, 0) AdS3 solutions of M-theory

We consider the most general solutions of eleven-dimensional supergravity preserving N = 2 supersymmetry whose metrics are warped products of three-dimensional anti-de Sitter space with an eight-dimensional manifold, focusing on those realising (2,0) superconformal symmetry. We give a set of necessary and sufficient conditions for a solution to be supersymmetric, which can be phrased, in the general case, in terms of a local SU(2) structure and its intrinsic torsion. We show that these supergravity backgrounds always admit a nowhere-vanishing Killing vector field that preserves the solution and encodes the U(1) R-symmetry of the dual field theory. We illustrate our results with examples which have appeared in the literature, including those with SU(4), G2 and SU(3) structures, and discuss new classes of Minkowski solutions.

Janus and Hades in M-theory

Multi-parametric and analytic families of four-dimensional AdS3 × ℝ (Janus) and AdS3 × ℝ+ (Hades) solutions are constructed in the SO(8) gauged supergravity that arises from the consistent reduction of eleven-dimensional supergravity on S7 . The solutions are generically non-supersymmetric, involve non-trivial running scalars and preserve a U(1)4 symmetry. Different patterns of (super) symmetry enhancement occur upon suitable adjustment of the free parameters which further control the boundary conditions of the running scalars. We concentrate on the non-supersymmetric Janus and Hades solutions with SU(3) × U(1)2 symmetry and provide their higher-dimensional description in terms of M-theory fluxes and membranes. Special attention is paid to a class of such Hades solutions dubbed “ridge flows” which resemble dielectric rotations of Coulomb branch flows previously investigated in the literature.

Maximally Twisted Eleven-Dimensional Supergravity

We perform the maximal twist of eleven-dimensional supergravity. This twist is partially topological and exists on manifolds of G_2 times SU(2) holonomy. Our derivation starts with an explicit description of the Batalin–Vilkovisky complex associated to the three-form multiplet in the pure spinor superfield formalism. We then determine the L_infty module structure of the supersymmetry algebra on the component fields. We twist the theory by modifying the differential of the Batalin–Vilkovisky complex to incorporate the action of a scalar supercharge. We find that the resulting free twisted theory is given by the tensor product of the de Rham and Dolbeault complexes of the respective G_2 and SU(2) holonomy manifolds as conjectured by Costello.

Consistent Kaluza-Klein Truncations and Two-Dimensional Gauged Supergravity.

We consider generalized Scherk-Schwarz reductions of E_{9} exceptional field theory to D=2 space-time dimensions and, in particular, construct the resulting scalar potential of all gauged supergravities that can be obtained in this way. This provides the first general expression for a multitude of theories with an interesting structure of vacua, covering potentially many new AdS_{2} cases. As an application, we prove the consistency of the truncation of eleven-dimensional supergravity on S^{8}×S^{1} to SO(9) gauged maximal supergravity. Fluctuations around its supersymmetric SO(9)-invariant vacuum describe holographically the dynamics of interacting D0-branes.

M2-branes wrapped on a topological disk

Employing the method applied to M5-branes recently by Bah, Bonetti, Minasian and Nardoni, we study M2-branes on a disk with non-trivial holonomies at the boundary. In four-dimensional U(1)4-gauged N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supergravity, we find supersymmetric AdS2 solutions from M2-branes wrapped on a topological disk in Calabi-Yau two-, three- and four-folds. We uplift the solutions to eleven-dimensional supergravity. For the solutions from topological disk in Calabi-Yau four-folds, the Bekenstein-Hawking entropy is finite and well-defined. On the other hand, from the topological disk in Calabi-Yau two- and three-folds, we could not find solutions with finite Bekenstein-Hawking entropy.

Generalizing eleven-dimensional supergravity

We develop a procedure to reproduce the ten-dimensional generalized supergravity equations from T-duality covariant equations, that facilitates generalization to U-duality covariant formulations of eleven-dimensional supergravity. The latter leads to a modification of the eleven-dimensional supergravity equations with terms that contain a rank-2 tensor field $J^{mn}$ which is the eleven-dimensional analog of the non-unimodularity Killing vector $I^m$ in ten dimensions.

D3-branes and M5-branes wrapped on a topological disc

Employing the method applied to construct AdS5 solutions from M5-branes recently by Bah, Bonetti, Minasian and Nardoni, we construct supersymmetric AdS3 solutions from D3-branes and M5-branes wrapped on a disc with non-trivial holonomies at the boundary. In five-dimensional U(1)3-gauged mathcal{N} = 2 supergravity, we find mathcal{N} = (2, 2) and mathcal{N} = (4, 4) supersymmetric AdS3 solutions. We uplift the solutions to type IIB supergravity and obtain D3-branes wrapped on a topological disc. We also uplift the solutions to eleven-dimensional supergravity and obtain M5-branes wrapped on a product of topological disc and Riemann surface. For the mathcal{N} = (2, 2) solution, holographic central charges are finite and well-defined. On the other hand, we could not find mathcal{N} = (4, 4) solution with finite holographic central charge. Finally, we show that the topological disc we obtain is, in fact, identical to a special case of the multi-charge spindle solution.

A Systematic Approach to Consistent Truncations of Supergravity Theories

Exceptional generalised geometry is a reformulation of eleven/ten-dimensional supergravity that unifies ordinary diffeomorphisms and gauge transformations of the higher-rank potentials of the theory in an extended notion of diffeormorphisms. These features make exceptional generalised geometry a very powerful tool to study consistent truncations of eleven/ten-dimensional supergravities. In this article, we review how the notion of generalised G-structure allows us to derive consistent truncations to supergravity theories in various dimensions and with different amounts of supersymmetry. We discuss in detail the truncations of eleven-dimensional supergravity to N=4 and N=2 supergravity in five dimensions.

On the squashed seven-sphere operator spectrum

We derive major parts of the eigenvalue spectrum of the operators on the squashed seven-sphere that appear in the compactification of eleven-dimensional supergravity. These spectra determine the mass spectrum of the fields in AdS4 and are important for the corresponding mathcal{N} = 1 supermultiplet structure. This work is a continuation of the work in [1] where the complete spectrum of irreducible isometry representations of the fields in AdS4 was derived for this compactification. Some comments are also made concerning the G2 holonomy and its implications on the structure of the operator equations on the squashed seven-sphere.

A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry

We consider a non-relativistic limit of the bosonic sector of eleven-dimensional supergravity, leading to a theory based on a covariant ‘membrane Newton-Cartan’ (MNC) geometry. The local tangent space is split into three ‘longitudinal’ and eight ‘transverse’ directions, related only by Galilean rather than Lorentzian symmetries. This generalises the ten-dimensional stringy Newton-Cartan (SNC) theory. In order to obtain a finite limit, the field strength of the eleven-dimensional four-form is required to obey a transverse self-duality constraint, ultimately due to the presence of the Chern-Simons term in eleven dimensions. The finite action then gives a set of equations that is invariant under longitudinal and transverse rotations, Galilean boosts and local dilatations. We supplement these equations with an extra Poisson equation, coming from the subleading action. Reduction along a longitudinal direction gives the known SNC theory with the addition of RR gauge fields, while reducing along a transverse direction yields a new non-relativistic theory associated to D2 branes. We further show that the MNC theory can be embedded in the U-duality symmetric formulation of exceptional field theory, demonstrating that it shares the same exceptional Lie algebraic symmetries as the relativistic supergravity, and providing an alternative derivation of the extra Poisson equation.

Components of eleven-dimensional supergravity with four off-shell supersymmetries

We derive the component structure of 11D, N = 1/8 supergravity linearized around eleven-dimensional Minkowski space. This theory represents 4 local supersymmetries closing onto 4 of the 11 spacetime translations without the use of equations of motion. It may be interpreted as adding 201 auxiliary bosons and 56 auxiliary fermions to the physical supergravity multiplet for a total of 376 + 376 components. These components and their transformations are organized into representations of SL(2; C) × G2.

Currents, charges and algebras in exceptional generalised geometry

A classical Ed(d)-invariant Hamiltonian formulation of world-volume theories of half-BPS p-branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to d ≤ 6. It consists of a Hamiltonian, characterised by a generalised metric, and a current algebra constructed s.t. it reproduces the Ed(d) generalised Lie derivative. Ed(d)-covariance necessitates the introduction of so-called charges, specifying the type of p-brane and the choice of section. For p > 2, currents of p-branes are generically non- geometric due to the imposition of U-duality, e.g. the M5-currents contain coordinates associated to the M2-momentum.A derivation of the Ed(d)-invariant current algebra from a canonical Poisson structure is in general not possible. At most, one can derive a current algebra associated to para-Hermitian exceptional geometry.The membrane in the SL(5)-theory is studied in detail. It is shown that in a generalised frame the current algebra is twisted by the generalised fluxes. As a consistency check, the double dimensional reduction from membranes in M-theory to strings in type IIa string theory is performed. Many features generalise to p-branes in SL(p + 3) generalised geometries that form building blocks for the Ed(d)-invariant currents.