Publications (22)117.75 Total impact
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ABSTRACT: The double copy is a muchstudied relationship between gauge theory and gravity amplitudes. Recently, this was generalised to an infinite family of classical solutions to Einstein's equations, namely stationary KerrSchild geometries. In this paper, we extend this to the TaubNUT solution in gravity, which has a double KerrSchild form. The single copy of this solution is a dyon, whose electric and magnetic charges are related to the mass and NUT charge in the gravity theory. Finally, we find hints that the classical double copy extends to curved background geometries.  [Show abstract] [Hide abstract]
ABSTRACT: We discuss the relation between perturbative gauge theory and perturbative gravity, and look at how this relation extends to some exact classical solutions. First, we give an overview of the double copy prescription that takes gauge theory amplitudes into gravity amplitudes, which has been crucial to progress in perturbative studies of supergravity. Then, we review how the selfdual sectors provide an important insight into the relation between the theories. A key role is played by a kinematic algebraic structure mirroring the color structure. Finally, we review how these ideas extend to some exact classical solutions, namely black holes and plane waves. 
Article: Black holes and the double copy
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ABSTRACT: Recently, a perturbative duality between gauge and gravity theories (the double copy) has been discovered, that is believed to hold to all loop orders. In this paper, we examine the relationship between classical solutions of nonAbelian gauge theory and gravity. We propose a general class of gauge theory solutions that double copy to gravity, namely those involving stationary KerrSchild metrics. The Schwarzschild and Kerr black holes (plus their higherdimensional equivalents) emerge as special cases. We also discuss plane wave solutions. Furthermore, a recently examined double copy between the selfdual sectors of YangMills theory and gravity can be reinterpreted using a momentumspace generalisation of the KerrSchild framework.  [Show abstract] [Hide abstract]
ABSTRACT: We study kinematic algebras associated to the recently proposed scattering equations, which arise in the description of the scattering of massless particles. In particular, we describe the role that these algebras play in the BCJ duality between colour and kinematics in gauge theory, and its relation to gravity. We find that the scattering equations are a consistency condition for a selfdualtype vertex which is associated to each solution of those equations. We also identify an extension of the antiselfdual vertex, such that the two vertices are not conjugate in general. Both vertices correspond to the structure constants of Lie algebras. We give a prescription for the use of the generators of these Lie algebras in trivalent graphs that leads to a natural set of BCJ numerators. In particular, we write BCJ numerators for each contribution to the amplitude associated to a solution of the scattering equations. This leads to a decomposition of the determinant of a certain kinematic matrix, which appears naturally in the amplitudes, in terms of trivalent graphs. We also present the kinematic analogues of colour traces, according to these algebras, and the associated decomposition of that determinant.  [Show abstract] [Hide abstract]
ABSTRACT: We present a systematic method to determine BCJ numerators for oneloop amplitudes that explores the global constraints on the loop momentum dependence. We apply this method to amplitudes in N=4 gauge theory, working out detailed examples up to seven points in both the MHV and the NMHV sectors. The structure of Jacobi identities between BCJ numerators is seen to be closely connected to that of algebraic integrand reductions. We discuss the consequences for oneloop N=8 supergravity amplitudes obtained through the double copy prescription. Moreover, in the MHV sector, we show how to obtain simple BCJ box numerators using a conjectured relationship to amplitudes in selfdual gauge theory. We also introduce simpler tracetype formulas for integrand reductions.  [Show abstract] [Hide abstract]
ABSTRACT: Colourkinematics duality is the conjecture of a group theorylike structure for the kinematic dependence of scattering amplitudes in gauge theory and gravity. This structure has been verified at tree level in various ways, but similar progress has been lacking at loop level, where the power of the duality would be most significant. Here we explore colourkinematics duality at one loop using the selfdual sector as a starting point. The duality is shown to exist in pure YangMills theory for two infinite classes of amplitudes: amplitudes with any number of particles either all of the same helicity or with one particle helicity opposite the rest. We provide a simple Lagrangianbased argument in favour of the double copy relation between gauge theory and gravity amplitudes in these classes, and provide some explicit examples. We further discuss aspects of the duality which persist after integration, leading to relations among partial amplitudes. Finally, we describe form factors in the selfdual theory at tree level which also satisfy the duality.  [Show abstract] [Hide abstract]
ABSTRACT: We study in detail a variety of gravitational toy models for hyperscalingviolating Lifshitz (hvLif) spacetimes. These spacetimes have been recently explored as holographic dual models for condensed matter systems. We start by considering a model of gravity coupled to a massive vector field and a dilaton with a potential. This model supports the full class of hvLif spacetimes and special attention is given to the particular values of the scaling exponents appearing in certain nonFermi liquids. We study linearized perturbations in this model, and consider probe fields whose interactions mimic those of the perturbations. The resulting equations of motion for the probe fields are invariant under the Lifshitz scaling. We derive BreitenlohnerFreedmantype bounds for these new probe fields. For the cases of interest the hvLif spacetimes have curvature invariants that blow up in the UV. We study the problem of constructing models in which the hvLif spacetime can have an AdS or Lifshitz UV completion. We also analyze reductions of Schroedinger spacetimes and reductions of waves on extremal (intersecting) branes, accompanied by transverse space reductions, that are solutions to supergravitylike theories, exploring the allowed parameter range of the hvLif scaling exponents. 
Article: Algebras for Amplitudes
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ABSTRACT: Treelevel amplitudes of gauge theories are expressed in a basis of auxiliary amplitudes with only cubic vertices. The vertices in this formalism are explicitly factorized in color and kinematics, clarifying the colorkinematics duality in gauge theory amplitudes. The basis is constructed making use of the KK and BCJ relations, thereby showing precisely how these relations underlie the colorkinematics duality. We express gravity amplitudes in terms of a related basis of colordressed gauge theory amplitudes, with basis coefficients which are permutation symmetric.  [Show abstract] [Hide abstract]
ABSTRACT: We use a mix of analytic and numerical methods to exhaustively study a class of asymptotically global AdS solitons and hairy black hole solutions in negative cosmological constant Einstein Maxwell gravity coupled to a charged massless scalar field. Our results depend sensitively on the charge 'e' of the scalar field. The solitonic branch of solutions we study hit the Chandrashekhar limit at finite mass at small 'e', but extends to arbitrarily large mass at larger 'e'. At low values of 'e' no hairy black holes exist. At intermediate values of 'e' hairy black holes exist above a critical charge. At large 'e' hairy black holes exist at all values of the charge. The lowest mass hairy black holes is a smooth zero entropy soliton at small charge, but a (probably) singular nonzero entropy hairy black hole at larger charge. In a phase diagram of solutions, the hairy black holes merge with the familiar ReissnerNordstromAdS black holes along a curve that is determined by the onset of the superradiant instability in the latter family.  [Show abstract] [Hide abstract]
ABSTRACT: We study linearized perturbations of MyersPerry black holes in d=7, with two of the three angular momenta set to be equal, and show that instabilities always appear before extremality. Analogous results are expected for all higher odd d. We determine numerically the stationary perturbations that mark the onset of instability for the modes that preserve the isometries of the background. The onset is continuously connected between the previously studied sectors of solutions with a single angular momentum and solutions with all angular momenta equal. This shows that the nearextremality instabilities are of the same nature as the ultraspinning instability of d>5 singlyspinning solutions, for which the angular momentum is unbounded. Our results raise the question of whether there are any extremal MyersPerry black holes which are stable in d>5.  [Show abstract] [Hide abstract]
ABSTRACT: We identify a diffeomorphism Lie algebra in the selfdual sector of YangMills theory, and show that it determines the kinematic numerators of treelevel MHV amplitudes in the full theory. These amplitudes can be computed offshell from Feynman diagrams with only cubic vertices, which are dressed with the structure constants of both the YangMills colour algebra and the diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We further study perturbative gravity, both in the selfdual and in the MHV sectors, finding that the kinematic numerators of the theory are the BCJ squares of the YangMills numerators.  [Show abstract] [Hide abstract]
ABSTRACT: It has recently been proposed that the strong coupling behaviour of quantum field theories on a nondynamical black hole background can be described, in the context of the AdS/CFT correspondence, by a competition between two gravity duals: a black funnel and a black droplet. We present here thermal equilibrium solutions which represent such spacetimes, providing the first example where the thermal competition between the gravity duals can be studied. The solutions correspond to a special family of charged AdS Cmetrics. We compute the corresponding Euclidean actions and find that the black funnel always dominates the canonical ensemble in our example, meaning that the field theory does not undergo a phase transition.  [Show abstract] [Hide abstract]
ABSTRACT: MyersPerry black holes with a single spin in d > 5 have been shown to be unstable if rotating sufficiently rapidly. We extend the numerical analysis which allowed for that result to the asymptotically AdS case. We determine numerically the stationary perturbations that mark the onset of the instabilities for the modes that preserve the rotational symmetries of the background. The parameter space of solutions is thoroughly analysed, and the onset of the instabilities is obtained as a function of the cosmological constant. Each of these perturbations has been conjectured to represent a bifurcation point to a new phase of stationary AdS black holes, and this is consistent with our results. KeywordsBlack Holes in String Theory–AdSCFT Correspondence–Black Holes  [Show abstract] [Hide abstract]
ABSTRACT: We study the effect of marginal and irrelevant deformations on the renormalization of operators near a CFT fixed point. New divergences in a given operator are determined by its OPE with the operator D that generates the deformation. This provides a scheme to compute the couplings a_DAB between the operator D and two arbitrary operators O_A and O_B. We exemplify for the case of N=4 SYM, considering the simplest case of the exact Lagrangian deformation. In this case the deformed anomalous dimension matrix is determined by the derivative of the anomalous dimension matrix with respect to the coupling. We use integrability techniques to compute the oneloop couplings a_LAB between the Lagrangian and two distinct large operators built with Magnons, in the SU(2) sector of the theory. Then we consider a_DAA at strong coupling, and show how to compute it using the gauge/gravity duality, when D is a chiral operator dual to any supergravity field and O_A is dual to a heavy string state. We exemplify for the Lagrangian and operators O_A dual to heavy string states, showing agreement with the prediction derived from the renormalization group arguments. Comment: 31 pages, 1 figure  [Show abstract] [Hide abstract]
ABSTRACT: Nearextreme ReissnerNordstromantide Sitter black holes are unstable against the condensation of an uncharged scalar field with mass close to the BreitenlohnerFreedman bound. It is shown that a similar instability afflicts nearextreme large rotating AdS black holes, and nearextreme hyperbolic SchwarzschildAdS black holes. The resulting nonlinear hairy black hole solutions are determined numerically. Some stability results for (possibly charged) scalar fields in black hole backgrounds are proved. For most of the extreme black holes we consider, these demonstrate stability if the ``effective mass" respects the nearhorizon BF bound. Small spherical ReissnerNordstromAdS black holes are an interesting exception to this result. Comment: 34 pages; 13 figures  [Show abstract] [Hide abstract]
ABSTRACT: Rapidly rotating MyersPerry black holes in d>5 dimensions were conjectured to be unstable by Emparan and Myers. In a previous publication, we found numerically the onset of the axisymmetric ultraspinning instability in the singlyspinning MyersPerry black hole in d=7,8,9. This threshold signals also a bifurcation to new branches of axisymmetric solutions with pinched horizons that are conjectured to connect to the black ring, black Saturn and other families in the phase diagram of stationary solutions. We firmly establish that this instability is also present in d=6 and in d=10,11. The boundary conditions of the perturbations are discussed in detail for the first time and we prove that they preserve the angular velocity and temperature of the original MyersPerry black hole. This property is fundamental to establish a thermodynamic necessary condition for the existence of this instability in general rotating backgrounds. We also prove a previous claim that the ultraspinning modes cannot be pure gauge modes. Finally we find new ultraspinning GregoryLaflamme instabilities of rotating black strings and branes that appear exactly at the critical rotation predicted by the aforementioned thermodynamic criterium. The latter is a refinement of the GubserMitra conjecture. Comment: 38 pages, 6 figures, 1 table  [Show abstract] [Hide abstract]
ABSTRACT: We present the first example of a linearized gravitational instability of an asymptotically flat vacuum black hole. We study perturbations of a MyersPerry black hole with equal angular momenta in an odd number of dimensions. We find no evidence of any instability in five or seven dimensions, but in nine dimensions, for sufficiently rapid rotation, we find perturbations that grow exponentially in time. The onset of instability is associated with the appearance of timeindependent perturbations which generically break all but one of the rotational symmetries. This is interpreted as evidence for the existence of a new 70parameter family of black hole solutions with only a single rotational symmetry. We also present results for the GregoryLaflamme instability of rotating black strings, demonstrating that rotation makes black strings more unstable. Comment: 38 pages, 13 figures  [Show abstract] [Hide abstract]
ABSTRACT: We study the thermodynamic stability of the Kerrantide Sitter black hole from the perturbative corrections to the gravitational partition function. The line of critical stability is identified by the appearance of a negative mode of the Euclidean action that renders the partition function ill defined. The eigenvalue problem, consisting of a system of three coupled partial differential equations for the metric perturbations, is solved numerically. The agreement with the standard condition of thermodynamic stability in the grandcanonical ensemble is remarkable. The results illustrate the physical significance of gravitational partition functions for rotating spacetimes beyond the instanton approximation. At a classical level, the results also imply that the GregoryLaflamme instability of the Kerr string persists up to extremality, the range of unstable modes increasing with the angular momentum.  [Show abstract] [Hide abstract]
ABSTRACT: We show that the quasiEuclidean sections of various rotating black holes in different dimensions possess at least one nonconformal negative mode when thermodynamic instabilities are expected. The boundary conditions of the fixed induced metric correspond to the partition function of the grandcanonical ensemble. Indeed, in the asymptotically flat cases, we find that a negative mode persists even if the specific heat at constant angular momenta is positive, since the stability in this ensemble also requires the positivity of the isothermal moment of inertia. We focus, in particular, on Kerr black holes, on MyersPerry black holes in five and six dimensions, and on the EmparanReall black ring solution. We go on further to consider the richer case of the asymptotically AdS Kerr black hole in four dimensions, where thermodynamic stability is expected for a large enough cosmological constant. The results are consistent with previous findings in the nonrotation limit and support the use of quasiEuclidean instantons to construct gravitational partition functions.  [Show abstract] [Hide abstract]
ABSTRACT: It has been conjectured that higherdimensional rotating black holes become unstable at a sufficiently large value of the rotation, and that new black holes with pinched horizons appear at the threshold of the instability. We search numerically, and find, the stationary axisymmetric perturbations of MyersPerry black holes with a single spin that mark the onset of the instability and the appearance of the new black hole phases. We also find new ultraspinning GregoryLaflamme instabilities of rotating black strings and branes. Comment: 5 pages, 5 figures. The instability of the black hole is argued to appear at the second zero mode. The first zero mode is not associated to a new branch of black hole solutions
Publication Stats
715  Citations  
117.75  Total Impact Points  
Top Journals
Institutions

20132015

University of Oxford
 Mathematical Institute
Oxford, England, United Kingdom


20112013

IT University of Copenhagen
København, Capital Region, Denmark


20092010

University of Cambridge
 Department of Applied Mathematics and Theoretical Physics
Cambridge, England, United Kingdom
