We describe a systematic framework for computing the conservative potential of a compact binary system using modern tools from scattering amplitudes and effective field theory. Our approach combines methods for integration and matching adapted from effective field theory, generalized unitarity, and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. With these methods we derive the third post-Minkowskian correction to the conservative two-body Hamiltonian for spinless black holes. We describe in some detail various checks of our integration methods and the resulting Hamiltonian.
We show how to double-copy Heavy Quark Effective Theory (HQET) to Heavy Black Hole Effective Theory (HBET) for spin $s\leq 1$. In particular, the double copy of spin-$s$ HQET with scalar QCD produces spin-$s$ HBET, while the double copy of spin-1/2 HQET with itself gives spin-1 HBET. Finally, we present novel all-order-in-mass Lagrangians for spin-1 heavy particles.
The classical double copy relating exact solutions of biadjoint scalar, gauge and gravity theories continues to receive widespread attention. Recently, a derivation of the exact classical double copy was presented, using ideas from twistor theory, in which spacetime fields are mapped to Cech cohomology classes in twistor space. A puzzle remains, however, in how to interpret the twistor double copy, in that it relies on somehow picking special representatives of each cohomology class. In this paper, we provide two alternative formulations of the twistor double copy using the more widely-used la…
The double copy is a much-studied relationship between gauge theory and gravity amplitudes. Recently, this was generalised to an infinite family of classical solutions to Einstein's equations, namely stationary Kerr-Schild geometries. In this paper, we extend this to the Taub-NUT solution in gravity, which has a double Kerr-Schild 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.
The Weyl double copy is a procedure for relating exact solutions in biadjoint scalar, gauge and gravity theories, and relates fields in spacetime directly. Where this procedure comes from, and how general it is, have until recently remained mysterious. In this paper, we show how the current form and scope of the Weyl double copy can be derived from a certain procedure in twistor space. The new formalism shows that the Weyl double copy is more general than previously thought, applying in particular to gravity solutions with arbitrary Petrov types. We comment on how to obtain anti-self-dual as w…
We construct classical curvature spinors in topologically massive gauge theory and topologically massive gravity, expressed in terms of massive three-particle amplitudes. We show that when the amplitudes double copy, the curvature spinors satisfy the Cotton double copy, the three-dimensional cousin of the Weyl double copy. Furthermore, we show that under certain circumstances the Cotton double copy can be derived via a dimensional reduction of the Weyl double copy.
The double copy is a map from non-abelian gauge theories to gravity, that has been demonstrated both for scattering amplitudes and exact classical solutions. In this study, we reconsider the double copy for exact solutions that are self-dual in either the gauge or gravity theory. In this case, one may formulate a general double copy in terms of a certain differential operator, which generates the gauge and gravity solutions from a harmonic function residing in a biadjoint scalar theory. As an illustration, we examine the single copy of the well-known Eguchi-Hanson instanton in gravity. The gau…
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 non-Abelian gauge theory and gravity. We propose a general class of gauge theory solutions that double copy to gravity, namely those involving stationary Kerr-Schild metrics. The Schwarzschild and Kerr black holes (plus their higher-dimensional equivalents) emerge as special cases. We also discuss plane wave solutions. Furthermore, a recently examined double copy between …
The naive double-copy of (multi) loop amplitudes involving massive matter coupled to gauge theories will generically produce amplitudes in a gravitational theory that contains additional contributions from propagating antisymmetric tensor and dilaton states even at tree-level. We present a graph-based approach that combines the method of maximal cuts with double-copy construction to offer a systematic framework to isolate the pure Einstein-Hilbert gravitational contributions through loop level. Indeed this allows for a bootstrap of pure-gravitational results from the double-copy of massive sca…
We extend Shen's recent formulation (arXiv:1806.07388) of the classical double copy, based on explicit color-kinematic duality, to the case of finite-size sources with non-zero spin. For the case of spinning Yang-Mills sources, the most general consistent double copy consists of gravitating objects which carry pairs of spin degrees of freedom. We find that the couplings of such objects to background fields match those of a classical (i.e. heavy) closed bosonic string, suggesting a string theory interpretation of sources related by color-kinematics duality. As a special case, we identify a limi…
The Weyl double copy relates vacuum solutions in general relativity to Abelian gauge fields in Minkowski spacetime. In a previous work, we showed how the Weyl double copy can be extended to provide a treatment of external gravitational sources consistent with the classical Kerr-Schild double copy. Using this generalization, here we provide a complete double copy analysis of electrovacuum Petrov type D spacetimes. This includes the first analysis of the charged C-metric, whose single copy interpretation invokes the two-potential formalism of electrodynamics. We also present the first double cop…
We construct a double copy relation between the Cotton spinor and the dual field strength spinor of topologically massive theories, as the three-dimensional analogue of the Weyl double copy. The relationship holds in curved backgrounds for wave solutions. We give an explicit proof for Type N spacetimes and show examples satisfying the Cotton double copy.
We establish a correspondence between perturbative classical gluon and gravitational radiation emitted by spinning sources, to linear order in spin. This is an extension of the non-spinning classical perturbative double copy and uses the same color-to-kinematic replacements. The gravitational theory has a scalar (dilaton) and a 2-form field (the Kalb-Ramon axion) in addition to the graviton. In arXiv:1712.09250, we computed axion radiation in the gravitational theory to show that the correspondence fixes its action. Here, we present complete details of the gravitational computation. In particu…
The classical double copy relates solutions to the equations of motion in gauge theory and in gravity. In this paper, we present two double-copy formalisms for relating the Coulomb solution in gauge theory to the two-parameter Janis-Newman-Winicour solution in gravity. The latter is a static, spherically symmetric, asymptotically flat solution that generically includes a dilaton field, but also admits the Schwarzschild solution as a special case. We first present the classical double copy as a perturbative construction, similar to its formulation for scattering amplitudes, and then present it …
The Weyl double copy relates exact solutions in general relativity to exact solutions in gauge theory, formulated in the spinorial language. To date, the Weyl double copy is understood and employed only for vacuum spacetimes, and hence only to vacuum gauge theories. In this letter, we propose an extension to the Weyl double copy that provides a systematic procedure for treating gravitational sources. We show this extended Weyl double copy gives a new perspective on the Kerr-Newman black hole and the general class of Petrov type D electro-vac spacetimes.
We extend the perturbative classical double copy to the analysis of bound systems. We first obtain the leading order perturbative gluon radiation field sourced by a system of interacting color charges in arbitrary time dependent orbits, and test its validity by taking relativistic bremsstrahlung and non-relativistic bound state limits. By generalizing the color to kinematic replacement rules recently used in the context of classical bremsstrahlung, we map the gluon emission amplitude to the radiation fields of dilaton gravity sourced by interacting particles in generic (self-consistent) orbits…
We derive a non-perturbative, Lagrangian-level formulation of the double copy in two spacetime dimensions. Our results elucidate the field theoretic underpinnings of the double copy in a broad class of scalar theories which can include masses and higher-dimension operators. An immediate corollary is the amplitudes-level double copy at all orders in perturbation theory. Applied to certain integrable models, the double copy defines an isomorphism between Lax connections, Wilson lines, and infinite towers of conserved currents. We also implement the double copy at the level of non-perturbative cl…
We find double copy relations between classical radiating solutions in Yang-Mills theory coupled to dynamical color charges and their counterparts in a cubic bi-adjoint scalar field theory which interacts linearly with particles carrying bi-adjoint charge. The particular color-to-kinematics replacements we employ are motivated by the BCJ double copy correspondence for on-shell amplitudes in gauge and gravity theories. They are identical to those recently used to establish relations between classical radiating solutions in gauge theory and in dilaton gravity. Our explicit bi-adjoint solutions a…
We construct the pure gravity Becchi-Rouet-Stora-Tyutin (BRST) Einstein-Hilbert Lagrangian, to cubic order, using the BRST convolution product of two Yang-Mills theories, in conjunction with the Bern-Carrasco-Johansson (BCJ) double-copy.
A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that the Weyl double copy holds asymptotically in cases where the full solution is algebraically general, using rotating STU supergravity black holes as an example. The asymptotic formulation provides clues regarding the relation between asymptotic symmetries that follows from the double copy. Using the C-metric as an example, we show that a previous interpretation of this gravity solution as a superrotation has a single copy analogue relating the appropriate Liénard-Wiechert potential to a l…
The classical double copy relates exact solutions of gauge, gravity and other theories. Although widely studied, its origins and domain of applicability have remained mysterious. In this letter, we show that a particular incarnation - the Weyl double copy - can be derived using well-established ideas from twistor theory. As well as explaining where the Weyl double copy comes from, the twistor formalism also shows that it is more general than previously thought.
The recently developed worldline quantum field theory (WQFT) formalism for the classical gravitational scattering of massive bodies is extended to massive, charged point particles coupling to bi-adjoint scalar field theory, Yang-Mills theory, and dilaton-gravity. We establish a classical double copy relation in these WQFTs for classical observables (deflection, radiation). The bi-adjoint scalar field theory fixes the locality structure of the double copy from Yang-Mills to dilaton-gravity. Using this the eikonal scattering phase (or free energy of the WQFT) is computed to next-to-leading order…
The double copy is a much-studied relationship between scattering amplitudes in gauge and gravity theories, that has subsequently been extended to classical field solutions. In nearly all previous examples, the graviton field is defined around Minkowski space. Recently, it has been suggested that one may set up a double copy for gravitons defined around a non-trivial background. We investigate this idea from the point of view of the classical double copy. First, we use Kerr-Schild spacetimes to construct graviton solutions in curved space, as double copies of gauge fields on non-zero gauge bac…
Gauge-gravity duality is arguably our best hope for understanding quantum gravity. Considerable progress has been made in relating scattering amplitudes in certain gravity theories to those in gauge theories---a correspondence dubbed the "double copy". Recently, double copies have also been realized in a classical setting, as maps between exact solutions of gauge theories and gravity. We present here a novel map between a certain class of real, exact solutions of Einstein's equations and self-dual solutions of the flat-space vacuum Maxwell equations. This map, which we call the "Newman-Penrose…
Here we discuss color-kinematics duality for higher-derivative QCD-like amplitudes. We explicitly show that the duality still holds in this case and it can be instrumental in constructing the associated quadratic-gravity amplitudes by using the double-copy prescription. This allows one to drastically simplify calculations. We also evaluate some tree-level Compton scattering amplitudes in higher-derivative Yang-Mills and quadratic gravity coupled with matter. Furthermore, we illustrate the application of generalized unitarity method for both cases by studying a specific one-loop amplitude.
Advances in our understanding of perturbation theory suggest the existence of a correspondence between classical general relativity and Yang-Mills theory. A concrete example of this correspondence, which is known as the double copy, was recently introduced for the case of stationary Kerr-Schild spacetimes. Building on this foundation, we examine the simple time-dependent case of an accelerating, radiating point source. The gravitational solution, which generalises the Schwarzschild solution, includes a non-trivial stress-energy tensor. This stress-energy tensor corresponds to a gauge theoretic…
Recently, a double-copy formalism was used to calculate gravitational radiation from classical Yang-Mills radiation solutions. This work shows that Yang-Mills theory coupled to a biadjoint scalar field admits a radiative double copy that agrees with solutions in Einstein-Yang-Mills theory at the lowest finite order. Within this context, the trace-reversed metric $\bar{h}^{μν}$ is a natural double copy of the gauge boson $A^{μa}$. This work provides additional evidence that solutions in gauge and gravity theories are related, even though their respective Lagrangians and nonlinear equations of m…
Recently, an intriguing relationship (the "double copy") has been discovered between theories like electromagnetism, and gravity. This potentially gives us a new way to think about gravity, and there are also practical applications involving the efficient calculation of gravitational observables, and also how to simulate gravity using optical systems. In this tutorial, we will review what is known about the double copy, and argue that now is the perfect time for researchers in optics and / or condensed matter to become interested in this fascinating correspondence.
We examine the double copy structure of anyons in gauge theory and gravity. Using on-shell amplitude techniques, we construct little group covariant spinor-helicity variables describing massive particles with spin, which together with locality and unitarity enables us to derive the long-range tree-level scattering amplitudes involving anyons. We discover that classical gauge theory anyon solutions double copy to their gravitational counterparts in a non-trivial manner. Interestingly, we show that the massless double copy captures the topological structure of curved spacetime in three dimension…
MIT Center for theoretical physics（麻省理工学院理论物理中心）；INFN Sezione di Firenze（意大利国家核物理研究所佛罗伦萨分部）；Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文系）；Centre for Geometry and Physics, Uppsala University（乌普萨拉大学几何与物理中心）
We argue that the complex transformation relating the Schwarzschild to the Taub-NUT metric, introduced by Talbot, is in fact an electric-magnetic duality transformation. We show that at null infinity, the complex transformation is equivalent to a complexified BMS supertranslation, which rotates the supertranslation and the dual (magnetic) supertranslation charges. This can also be seen from the cubic coupling between the classical source and its background, which for Taub-NUT is given by a complex phase rotation acting on gravitational minimal couplings. The same phase rotation generates dyons…
We formulate a new program to generalize the double-copy of tree amplitudes. The approach exploits the link between the identity element of the KLT algebra and the KLT kernel, and we demonstrate how this leads to a set of KLT bootstrap equations that the double-copy kernel has to satisfy (in addition to locality constraints). We solve the KLT bootstrap equations perturbatively to find the most general higher-derivative corrections to the 4- and 5-point field theory KLT kernel. The new kernel generalizes the string KLT kernel and its associated monodromy relations. It admits new color-structure…
We consider the momentum-space 3-point correlators of currents, stress tensors and marginal scalar operators in general odd-dimensional conformal field theories. We show that the flat space limit of these correlators is spanned by gauge and gravitational scattering amplitudes in one higher dimension which are related by a double copy. Moreover, we recast three-dimensional CFT correlators in terms of tree-level Feynman diagrams without energy conservation, suggesting double copy structure beyond the flat space limit.
We study the scattering amplitudes of massive Kaluza-Klein (KK) states of open and closed bosonic strings under toroidal compactification. We analyze the structure of vertex operators for the KK strings and derive an extended massive KLT-like relation which connects the $N$-point KK closed-string amplitude to the products of two KK open-string amplitudes at tree level. Taking the low energy field-theory limit of vanishing Regge slope, we derive double-copy construction formula of the $N$-point massive KK graviton amplitude from the sum of proper products of the corresponding KK gauge boson amp…
We find that scattering amplitudes in massive scalar QCD can manifest the duality between color and kinematics at loop-level. Specifically we construct the one-loop integrands for four-point scattering between two distinct massive scalars, and the five-point process encoding the first correction to massive scalar scattering with gluonic radiation. We find that factorization and the color-kinematics duality are sufficient principles to entirely bootstrap these calculations, allowing us to construct all contributions ultimately from the three-point tree-level amplitudes which are themselves enti…
We construct entangled states of gluons that scatter exactly as if they were gravitons. Operationally, these objects implement the double copy at the level of the wave function. Our analysis begins with a general ansatz for a wave function characterizing gluons in two copies of ${\rm SU}(N)$ gauge theory. Given relatively minimal assumptions following from permutation invariance and dimensional analysis, the three- and four-particle wave functions generate scattering amplitudes that automatically coincide exactly with gravity, modulo normalization. For five-particle scattering the match is not…
The double copy relates momentum-space scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, where in some cases an exact double copy can be formulated directly in terms of products of fields in position space. This is seemingly at odds with the momentum-space origins of the double copy, and the question of why exact double copies are possible in position space and when this form will break has remained largely unanswered. In this paper, we provide an answer to this question, using a recently developed twistorial formulation of the double copy. …
Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California at Los Angeles（加州大学洛杉矶分校物理与天文学系马尼·L·布豪米克理论物理研究所）；Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London（伦敦玛丽女王大学物理与天文学院弦理论研究中心）；Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh（爱丁堡大学物理与天文学院希格斯理论物理中心）
We are investigating if the double copy structure as product of scattering amplitudes of gauge theories applies to cosmological correlators computed in a class of theories for inflation by the operatorial version of the In-In formalism of Schwinger-Keldysh. We consider tree level momentum-space correlators involving primordial gravitational waves with different polarizations and the scalar curvature fluctuations on a three dimensional fixed spatial slice. The correlators are sum of terms factorized in a time dependent scalar factor, which takes into account the curved background where energy i…
The classical double copy relations establish correspondence between exact gravity solutions and their counterparts in biadjoint and gauge theories. In this work, we investigate a peculiar case of double copy relations arising in exact solutions of the scalar gravity equation, relating static spacetime geometry to the Komar density distribution. We use a scalar-restricted static metric ansatz to isolate the degree of freedom governed by the linear equation for the zeroth copy. The corresponding metric solutions are interpreted as describing gravity without self-interaction, based on the Komar …
The Kerr-Schild double copy relates exact solutions of gauge and gravity theories. In all previous examples, the gravity solution is associated with an abelian-like gauge theory object, which linearises the Yang-Mills equations. This appears to be at odds with the double copy for scattering amplitudes, in which the non-abelian nature of the gauge theory plays a crucial role. Furthermore, it is not yet clear whether or not global properties of classical fields - such as non-trivial topology - can be matched between gauge and gravity theories. In this paper, we clarify these issues by explicitly…
The double copy relates scattering amplitudes in gauge and gravity theories, and has also been extended to classical solutions. In this paper, we study solutions in three spacetime dimensions, where the double copy may be expected to be problematic due to the absence of propagating degrees of freedom for the graviton, and the lack of a Newtonian limit. In particular, we examine the double copy of a gauge theory point charge. This is a vacuum solution in gauge theory, but leads to a non-vacuum solution in gravity, which we show is consistent with previously derived constraints. Furthermore, we …
