We apply the classical double copy procedure to a class of regular, non-singular black hole solutions. We give several examples, paying particular attention to a string-theory-corrected black hole solution emerging from T-duality. Non-perturbative stringy corrections introduce an ultraviolet (UV) zero-point length cutoff which results in non-singular black hole spacetimes. Apart from the UV regulator, the solution is equivalent to the Bardeen black hole spacetime. We extend this solution to include an asymptotic de Sitter background. All Yang-Mills field theory quantities associated with the double copy are well-behaved and finite for all values of parameters. We present a thorough analysis of the black hole horizon structure, additionally uncovering a simple yet new connection between horizons on the gravity side and electric fields on the gauge theory side of the double copy.
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 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.
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 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 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…
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）
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）
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…
We give a double copy construction for the symmetries of the self-dual sectors of Yang-Mills (YM) and gravity, in the light-cone formulation. We find an infinite set of double copy constructible symmetries. We focus on two families which correspond to the residual diffeomorphisms on the gravitational side. For the first one, we find novel non-perturbative double copy rules in the bulk. The second family has a more striking structure, as a non-perturbative gravitational symmetry is obtained from a perturbatively defined symmetry on the YM side. At null infinity, we find the YM origin of the sub…
We study the classical double copy for ungauged half-maximal supergravities using the Kaluza-Klein reduction of double field theory (DFT). We construct a general formula for the Kaluza-Klein (KK) reduction of the DFT Kerr-Schild ansatz. The KK reduction of the ansatz is highly nonlinear, but the associated equations of motion are linear. This linear structure implies that half-maximal supergravities admit a classical double copy. We show that their single copy is given by a pair of Maxwell-scalar theories, which are the KK reduction of a higher-dimensional single copy of DFT. We also investiga…
The three-point amplitude is the key building block in the on-shell approach to scattering amplitudes. We show that the classical objects computed by massive three-point amplitudes in gauge theory and gravity are Newman-Penrose scalars in a split-signature spacetime, where three-point amplitudes can be defined for real kinematics. In fact, the quantum state set up by the particle is a coherent state fully determined by the three-point amplitude due to an eikonal-type exponentiation. Having identified this simplest classical solution from the perspective of scattering amplitudes, we explore the…
The double copy is by now a firmly-established correspondence between amplitudes and classical solutions in biadjoint scalar, gauge and gravity theories. To date, no strongly coupled examples of the double copy in four dimensions have been found, and previous attempts based on exact non-linear solutions of biadjoint theory in Lorentzian signature have failed. In this paper, we instead look for biadjoint solutions in Euclidean signature, which may be relatable to Yang-Mills or gravitational instantons. We show that spherically symmetric power-like Euclidean solutions do not exist in precisely f…
Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学学院，UCAS）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；International Center for Theoretical Physics Asia-Pacific（亚太理论物理中心）
We extend the Kerr-Schild double copy to the case of a probe particle moving in the Kerr-Schild background. In particular, we solve Wong's equations for a test color charge in a Coulomb non-Abelian potential ($\sqrt{\text{Schw}}$) and on the equatorial plane for the potential generated by a rotating disk of charge known as the single copy of the $\text{Kerr}$ background ($\sqrt{\text{Kerr}}$). The orbits, as the corresponding geodesics on the gravity side, feature elliptic, circular, hyperbolic and plunge behaviour for the charged particle. We then find a new double copy map between the conser…
We give two double copy prescriptions which construct asymptotically flat solutions in gravity from asymptotically flat gauge fields. The first prescription applies to radiative fields, which are non-linear vacuum solutions determined by characteristic data at null infinity. For any two such radiative gauge fields (linear or non-linear), the characteristic data of a radiative metric, dilaton and axion is constructed by a simple `squaring' procedure, giving a classical double copy at the level of radiation fields. We demonstrate the procedure with several examples where the characteristic data …
Motivated by the results of Anastasiou et al., we consider the convolutional double copy for BRST and anti-BRST covariant formulations of gravitational and gauge theories in more detail. We give a general BRST and anti-BRST invariant formulation of linearised $\mathcal{N}=0$ supergravity using superspace methods and show how this may be obtained from the square of linearised Yang-Mills theories. We demonstrate this relation for the Schwarzschild black hole and the ten-dimensional black string solution as two concrete examples.
We construct the classical double copy formalism for M-theory. This extends the current state of the art by including the three form potential of eleven dimensional supergravity along with the metric. The key for this extension is to construct a Kerr-Schild type Ansatz for exceptional field theory. This Kerr-Schild Ansatz then allows us to find the solutions of charged objects such as the membrane from a set of single copy fields. The exceptional field theory formalism then automatically produces the IIB Kerr-Schild ansatz allowing the construction of the single copy for the fields of IIB supe…
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.
Similarity in the structure of scattering amplitudes in Yang-Mills theories and General Relativity led to the idea that graviton could be described as the double copy of a vector gauge field. In this letter we discuss a realization of this idea emerging directly from solutions of equations of General Relativity. A general form of the energy momentum tensor for the electric field is derived that leads to the metric tensor in terms of the double copy of a corresponding gauge potential. We than use this general property to find the double copy of spontaneously broken scalar electrodynamics. The r…
The double copy of the Coulomb solution in three dimensions is a non-vacuum solution that can be obtained through different matter couplings. It is the static black hole solution of Einstein-Maxwell theory or general relativity minimally coupled to a free scalar field (with one ghost sign in the action in both cases). We consider generalizations of these matter couplings by paying particular attention to the regularity of the static black solution on the gravity side and the corresponding single copy electric field in the gauge theory. We show that i) Einstein-Born-Infeld theory yields a singu…
We apply the classical double copy to the calculation of self-energy of composite systems with multipolar coupling to gravitational field, obtaining next-to-leading order results in the gravitational coupling $G_N$ by generalizing color to kinematics replacement rules known in literature. When applied to the multipolar description of the two-body system, the self-energy diagrams studied in this work correspond to tail processes, whose physical interpretation is of radiation being emitted by the non-relativistic source, scattered by the curvature generated by the binary system and then re-absor…
We explore various tree-level double copy constructions for amplitudes including massive particles with spin. By working in general dimensions, we use that particles with spins $s\leq 2$ are fundamental to argue that the corresponding double copy relations partially follow from compactification of their massless counterparts. This massless origin fixes the coupling of gluons, dilatons and axions to matter in a characteristic way (for instance fixing the gyromagnetic ratio), whereas the graviton couples universally reflecting the equivalence principle. For spin-1 matter we conjecture all-order …
