Abstract
The double copy relates scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, and a number of approaches have been developed for doing so. One of these involves expressing fields in a variety of (super-)gravity theories in terms of convolutions of gauge fields, including also BRST ghost degrees of freedom that map neatly to their corresponding counterparts in gravity. In this paper, we spell out how to use the convolutional double copy to map gauge and gravity solutions in the manifest Lorenz and de Donder gauges respectively. We then apply this to a particular example, namely the point charge in pure gauge theory. As well as clarifying how to use the convolutional approach, our results provide an alternative point of view on a recent discussion concerning whether point charges map to the Schwarzschild solution, or the more general two-parameter JNW solution, which includes a dilaton field. We confirm the latter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory, Phys. Rev. D 82 (2010) 065003 [arXiv:1004.0693] [INSPIRE].
R. Monteiro, D. O’Connell and C.D. White, Black holes and the double copy, JHEP 12 (2014) 056 [arXiv:1410.0239] [INSPIRE].
A. Luna, R. Monteiro, D. O’Connell and C.D. White, The classical double copy for Taub-NUT spacetime, Phys. Lett. B 750 (2015) 272 [arXiv:1507.01869] [INSPIRE].
A. Luna, R. Monteiro, I. Nicholson, D. O’Connell and C.D. White, The double copy: Bremsstrahlung and accelerating black holes, JHEP 06 (2016) 023 [arXiv:1603.05737] [INSPIRE].
N. Bahjat-Abbas, A. Luna and C.D. White, The Kerr-Schild double copy in curved spacetime, JHEP 12 (2017) 004 [arXiv:1710.01953] [INSPIRE].
D.S. Berman, E. Chacón, A. Luna and C.D. White, The self-dual classical double copy, and the Eguchi-Hanson instanton, JHEP 01 (2019) 107 [arXiv:1809.04063] [INSPIRE].
A.K. Ridgway and M.B. Wise, Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy, Phys. Rev. D 94 (2016) 044023 [arXiv:1512.02243] [INSPIRE].
M. Carrillo-González, R. Penco and M. Trodden, The classical double copy in maximally symmetric spacetimes, JHEP 04 (2018) 028 [arXiv:1711.01296] [INSPIRE].
M. Carrillo González, B. Melcher, K. Ratliff, S. Watson and C.D. White, The classical double copy in three spacetime dimensions, JHEP 07 (2019) 167 [arXiv:1904.11001] [INSPIRE].
N. Bahjat-Abbas, R. Stark-Muchão and C.D. White, Monopoles, shockwaves and the classical double copy, JHEP 04 (2020) 102 [arXiv:2001.09918] [INSPIRE].
L. Alfonsi, C.D. White and S. Wikeley, Topology and Wilson lines: global aspects of the double copy, JHEP 07 (2020) 091 [arXiv:2004.07181] [INSPIRE].
R. Alawadhi, D.S. Berman, B. Spence and D. Peinador Veiga, S-duality and the double copy, JHEP 03 (2020) 059 [arXiv:1911.06797] [INSPIRE].
R. Monteiro, I. Nicholson and D. O’Connell, Spinor-helicity and the algebraic classification of higher-dimensional spacetimes, Class. Quant. Grav. 36 (2019) 065006 [arXiv:1809.03906] [INSPIRE].
A. Luna, R. Monteiro, I. Nicholson and D. O’Connell, Type D Spacetimes and the Weyl Double Copy, Class. Quant. Grav. 36 (2019) 065003 [arXiv:1810.08183] [INSPIRE].
W.D. Goldberger and A.K. Ridgway, Radiation and the classical double copy for color charges, Phys. Rev. D 95 (2017) 125010 [arXiv:1611.03493] [INSPIRE].
W.D. Goldberger, S.G. Prabhu and J.O. Thompson, Classical gluon and graviton radiation from the bi-adjoint scalar double copy, Phys. Rev. D 96 (2017) 065009 [arXiv:1705.09263] [INSPIRE].
W.D. Goldberger and A.K. Ridgway, Bound states and the classical double copy, Phys. Rev. D 97 (2018) 085019 [arXiv:1711.09493] [INSPIRE].
W.D. Goldberger, J. Li and S.G. Prabhu, Spinning particles, axion radiation, and the classical double copy, Phys. Rev. D 97 (2018) 105018 [arXiv:1712.09250] [INSPIRE].
W.D. Goldberger and J. Li, Strings, extended objects, and the classical double copy, JHEP 02 (2020) 092 [arXiv:1912.01650] [INSPIRE].
A. Luna et al., Perturbative spacetimes from Yang-Mills theory, JHEP 04 (2017) 069 [arXiv:1611.07508] [INSPIRE].
A. Luna, I. Nicholson, D. O’Connell and C.D. White, Inelastic Black Hole Scattering from Charged Scalar Amplitudes, JHEP 03 (2018) 044 [arXiv:1711.03901] [INSPIRE].
B. Maybee, D. O’Connell and J. Vines, Observables and amplitudes for spinning particles and black holes, JHEP 12 (2019) 156 [arXiv:1906.09260] [INSPIRE].
L. Borsten and S. Nagy, The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order, JHEP 07 (2020) 093 [arXiv:2004.14945] [INSPIRE].
K. Lee, Kerr-Schild Double Field Theory and Classical Double Copy, JHEP 10 (2018) 027 [arXiv:1807.08443] [INSPIRE].
K. Kim, K. Lee, R. Monteiro, I. Nicholson and D. Peinador Veiga, The Classical Double Copy of a Point Charge, JHEP 02 (2020) 046 [arXiv:1912.02177] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, L.J. Hughes and S. Nagy, Yang-Mills origin of gravitational symmetries, Phys. Rev. Lett. 113 (2014) 231606 [arXiv:1408.4434] [INSPIRE].
A. Anastasiou et al., Twin supergravities from Yang-Mills theory squared, Phys. Rev. D 96 (2017) 026013 [arXiv:1610.07192] [INSPIRE].
G.L. Cardoso, S. Nagy and S. Nampuri, A double copy for \( \mathcal{N} \) = 2 supergravity: a linearised tale told on-shell, JHEP 10 (2016) 127 [arXiv:1609.05022] [INSPIRE].
G. Cardoso, S. Nagy and S. Nampuri, Multi-centered \( \mathcal{N} \) = 2 BPS black holes: a double copy description, JHEP 04 (2017) 037 [arXiv:1611.04409] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, A. Marrani, S. Nagy and M. Zoccali, Are all supergravity theories Yang-Mills squared?, Nucl. Phys. B 934 (2018) 606 [arXiv:1707.03234] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, A. Marrani, S. Nagy and M. Zoccali, The Mile High Magic Pyramid, Contemp. Math. 721 (2019) 1 [arXiv:1711.08476] [INSPIRE].
L. Borsten, M.J. Duff, L.J. Hughes and S. Nagy, Magic Square from Yang-Mills Squared, Phys. Rev. Lett. 112 (2014) 131601 [arXiv:1301.4176] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, L.J. Hughes and S. Nagy, A magic pyramid of supergravities, JHEP 04 (2014) 178 [arXiv:1312.6523] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Hughes and S. Nagy, Global symmetries of Yang-Mills squared in various dimensions, JHEP 01 (2016) 148 [arXiv:1502.05359] [INSPIRE].
Z. Bern, J.J. Carrasco, W.-M. Chen, H. Johansson and R. Roiban, Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes, Phys. Rev. Lett. 118 (2017) 181602 [arXiv:1701.02519] [INSPIRE].
Z. Bern, J.J.M. Carrasco, W.-M. Chen, H. Johansson, R. Roiban and M. Zeng, Five-loop four-point integrand of N = 8 supergravity as a generalized double copy, Phys. Rev. D 96 (2017) 126012 [arXiv:1708.06807] [INSPIRE].
H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
L.D. Faddeev and V.N. Popov, Feynman Diagrams for the Yang-Mills Field, Phys. Lett. B 25 (1967) 29 [INSPIRE].
C. Becchi, A. Rouet and R. Stora, The Abelian Higgs-Kibble Model. Unitarity of the S Operator, Phys. Lett. B 52 (1974) 344 [INSPIRE].
C. Becchi, A. Rouet and R. Stora, Renormalization of the Abelian Higgs-Kibble Model, Commun. Math. Phys. 42 (1975) 127 [INSPIRE].
C. Becchi, A. Rouet and R. Stora, Renormalization of Gauge Theories, Annals Phys. 98 (1976) 287 [INSPIRE].
I.V. Tyutin, Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism, arXiv:0812.0580 [INSPIRE].
E.S. Fradkin and G.A. Vilkovisky, Quantization of relativistic systems with constraints, Phys. Lett. B 55 (1975) 224 [INSPIRE].
I.A. Batalin and G.A. Vilkovisky, Relativistic S Matrix of Dynamical Systems with Boson and Fermion Constraints, Phys. Lett. B 69 (1977) 309 [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, S. Nagy and M. Zoccali, Gravity as Gauge Theory Squared: A Ghost Story, Phys. Rev. Lett. 121 (2018) 211601 [arXiv:1807.02486] [INSPIRE].
L. Borsten, I. Jubb, V. Makwana and S. Nagy, Gauge × gauge on spheres, JHEP 06 (2020) 096 [arXiv:1911.12324] [INSPIRE].
W. Siegel, Superstrings give old minimal supergravity, Phys. Lett. B 211 (1988) 55 [INSPIRE].
W. Siegel, Curved extended superspace from Yang-Mills theory a la strings, Phys. Rev. D 53 (1996) 3324 [hep-th/9510150] [INSPIRE].
G. Lopes Cardoso, G. Inverso, S. Nagy and S. Nampuri, Comments on the double copy construction for gravitational theories, PoS CORFU2017 (2018) 177 [arXiv:1803.07670] [INSPIRE].
L. Borsten, Gravity as the square of gauge theory: a review. Riv. Nuovo Cim. 43 (2020) 97 [INSPIRE].
A.I. Janis, E.T. Newman and J. Winicour, Reality of the Schwarzschild Singularity, Phys. Rev. Lett. 20 (1968) 878 [INSPIRE].
C.D. White, Exact solutions for the biadjoint scalar field, Phys. Lett. B 763 (2016) 365 [arXiv:1606.04724] [INSPIRE].
P.-J. De Smet and C.D. White, Extended solutions for the biadjoint scalar field, Phys. Lett. B 775 (2017) 163 [arXiv:1708.01103] [INSPIRE].
N. Bahjat-Abbas, R. Stark-Muchão and C.D. White, Biadjoint wires, Phys. Lett. B 788 (2019) 274 [arXiv:1810.08118] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2004.11254
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Luna, A., Nagy, S. & White, C.D. The convolutional double copy: a case study with a point. J. High Energ. Phys. 2020, 62 (2020). https://doi.org/10.1007/JHEP09(2020)062
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2020)062