Abstract
The double copy formalism provides an intriguing connection between gauge theories and gravity. It was first demonstrated in the perturbative context of scattering amplitudes but recently the formalism has been applied to exact classical solutions in gauge theories such as the monopole and instanton. In this paper we will investigate how duality symmetries in the gauge theory double copy to gravity and relate these to solution generating transformations and the action of SL(2, ℝ) in general relativity.
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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].
N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Minimal Basis for Gauge Theory Amplitudes, Phys. Rev. Lett. 103 (2009) 161602 [arXiv:0907.1425] [INSPIRE].
S. Stieberger, Open and Closed vs. Pure Open String Disk Amplitudes, arXiv:0907.2211 [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, T. Sondergaard and P. Vanhove, Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes, JHEP 06 (2010) 003 [arXiv:1003.2403] [INSPIRE].
B. Feng, R. Huang and Y. Jia, Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program, Phys. Lett. B 695 (2011) 350 [arXiv:1004.3417] [INSPIRE].
S.H. Henry Tye and Y. Zhang, Dual Identities inside the Gluon and the Graviton Scattering Amplitudes, JHEP 06 (2010) 071 [Erratum ibid. 1104 (2011) 114] [arXiv:1003.1732] [INSPIRE].
C.R. Mafra, O. Schlotterer and S. Stieberger, Explicit BCJ Numerators from Pure Spinors, JHEP 07 (2011) 092 [arXiv:1104.5224] [INSPIRE].
R. Monteiro and D. O’Connell, The Kinematic Algebra From the Self-Dual Sector, JHEP 07 (2011) 007 [arXiv:1105.2565] [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, R. Monteiro and D. O’Connell, Algebras for Amplitudes, JHEP 06 (2012) 061 [arXiv:1203.0944] [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].
Z. Bern, L.J. Dixon, D.C. Dunbar, M. Perelstein and J.S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys. B 530 (1998) 401 [hep-th/9802162] [INSPIRE].
M.B. Green, J.H. Schwarz and L. Brink, N = 4 Yang-Mills and N = 8 Supergravity as Limits of String Theories, Nucl. Phys. B 198 (1982) 474 [INSPIRE].
Z. Bern, J.S. Rozowsky and B. Yan, Two loop four gluon amplitudes in N = 4 superYang-Mills, Phys. Lett. B 401 (1997) 273 [hep-ph/9702424] [INSPIRE].
J.J.M. Carrasco and H. Johansson, Five-Point Amplitudes in N = 4 Super-Yang-Mills Theory and N = 8 Supergravity, Phys. Rev. D 85 (2012) 025006 [arXiv:1106.4711] [INSPIRE].
J.J.M. Carrasco, M. Chiodaroli, M. Günaydin and R. Roiban, One-loop four-point amplitudes in pure and matter-coupled N ≤ 4 supergravity, JHEP 03 (2013) 056 [arXiv:1212.1146] [INSPIRE].
C.R. Mafra and O. Schlotterer, The Structure of n-Point One-Loop Open Superstring Amplitudes, JHEP 08 (2014) 099 [arXiv:1203.6215] [INSPIRE].
R.H. Boels, R.S. Isermann, R. Monteiro and D. O’Connell, Colour-Kinematics Duality for One-Loop Rational Amplitudes, JHEP 04 (2013) 107 [arXiv:1301.4165] [INSPIRE].
N.E.J. Bjerrum-Bohr, T. Dennen, R. Monteiro and D. O’Connell, Integrand Oxidation and One-Loop Colour-Dual Numerators in N = 4 Gauge Theory, JHEP 07 (2013) 092 [arXiv:1303.2913] [INSPIRE].
Z. Bern, S. Davies, T. Dennen, Y.-t. Huang and J. Nohle, Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops, Phys. Rev. D 92 (2015) 045041 [arXiv:1303.6605] [INSPIRE].
Z. Bern, S. Davies and T. Dennen, The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops, Phys. Rev. D 88 (2013) 065007 [arXiv:1305.4876] [INSPIRE].
J. Nohle, Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter, Phys. Rev. D 90 (2014) 025020 [arXiv:1309.7416] [INSPIRE].
Z. Bern, S. Davies, T. Dennen, A.V. Smirnov and V.A. Smirnov, Ultraviolet Properties of N =4 Supergravity at Four Loops, Phys. Rev. Lett. 111(2013) 231302 [arXiv:1309.2498] [INSPIRE].
S.G. Naculich, H. Nastase and H.J. Schnitzer, All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes, JHEP 04 (2013) 114 [arXiv:1301.2234] [INSPIRE].
Y.-J. Du, B. Feng and C.-H. Fu, Dual-color decompositions at one-loop level in Yang-Mills theory, JHEP 06 (2014) 157 [arXiv:1402.6805] [INSPIRE].
C.R. Mafra and O. Schlotterer, Towards one-loop SYM amplitudes from the pure spinor BRST cohomology, Fortsch. Phys. 63 (2015) 105 [arXiv:1410.0668] [INSPIRE].
Z. Bern, S. Davies and T. Dennen, Enhanced ultraviolet cancellations in \( \mathcal{N} \) = 5 supergravity at four loops, Phys. Rev. D 90 (2014) 105011 [arXiv:1409.3089] [INSPIRE].
C.R. Mafra and O. Schlotterer, Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace, JHEP 10 (2015) 124 [arXiv:1505.02746] [INSPIRE].
S. He, R. Monteiro and O. Schlotterer, String-inspired BCJ numerators for one-loop MHV amplitudes, JHEP 01 (2016) 171 [arXiv:1507.06288] [INSPIRE].
Z. Bern, S. Davies and J. Nohle, Double-Copy Constructions and Unitarity Cuts, Phys. Rev. D 93 (2016) 105015 [arXiv:1510.03448] [INSPIRE].
G. Mogull and D. O’Connell, Overcoming Obstacles to Colour-Kinematics Duality at Two Loops, JHEP 12 (2015) 135 [arXiv:1511.06652] [INSPIRE].
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies, JHEP 06 (2017) 064 [arXiv:1511.01740] [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. Johansson and A. Ochirov, Color-Kinematics Duality for QCD Amplitudes, JHEP 01 (2016) 170 [arXiv:1507.00332] [INSPIRE].
S. Oxburgh and C.D. White, BCJ duality and the double copy in the soft limit, JHEP 02 (2013) 127 [arXiv:1210.1110] [INSPIRE].
C.D. White, Factorization Properties of Soft Graviton Amplitudes, JHEP 05 (2011) 060 [arXiv:1103.2981] [INSPIRE].
S. Melville, S.G. Naculich, H.J. Schnitzer and C.D. White, Wilson line approach to gravity in the high energy limit, Phys. Rev. D 89 (2014) 025009 [arXiv:1306.6019] [INSPIRE].
A. Luna, S. Melville, S.G. Naculich and C.D. White, Next-to-soft corrections to high energy scattering in QCD and gravity, JHEP 01 (2017) 052 [arXiv:1611.02172] [INSPIRE].
R. Saotome and R. Akhoury, Relationship Between Gravity and Gauge Scattering in the High Energy Limit, JHEP 01 (2013) 123 [arXiv:1210.8111] [INSPIRE].
A. Sabio Vera, E. Serna Campillo and M.A. Vazquez-Mozo, Color-Kinematics Duality and the Regge Limit of Inelastic Amplitudes, JHEP 04 (2013) 086 [arXiv:1212.5103] [INSPIRE].
H. Johansson, A. Sabio Vera, E. Serna Campillo and M. Á. Vázquez-Mozo, Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction, JHEP 10 (2013) 215 [arXiv:1307.3106] [INSPIRE].
H. Johansson, A. Sabio Vera, E. Serna Campillo and M. Á. Vazquez-Mozo, Color-kinematics duality and dimensional reduction for graviton emission in Regge limit, in International Workshop on Low X Physics (Israel 2013), Eilat Israel (2013) [arXiv:1310.1680] [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].
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].
S. Sabharwal and J.W. Dalhuisen, Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor, JHEP 07 (2019) 004 [arXiv:1904.06030] [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].
L. Borsten and M.J. Duff, Gravity as the square of Yang-Mills?, Phys. Scripta 90 (2015) 108012 [arXiv:1602.08267] [INSPIRE].
A. Anastasiou et al., Twin supergravities from Yang-Mills theory squared, Phys. Rev. D 96 (2017) 026013 [arXiv:1610.07192] [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].
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].
L. Borsten, D = 6, \( \mathcal{N} \) = (2, 0) and \( \mathcal{N} \) = (4, 0) theories, Phys. Rev. D 97 (2018) 066014 [arXiv:1708.02573] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, A. Marrani, S. Nagy and M. Zoccali, The Mile High Magic Pyramid, arXiv:1711.08476 [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].
G. Lopes Cardoso, G. Inverso, S. Nagy and S. Nampuri, Comments on the double copy construction for gravitational theories, PoS(CORFU2017)177 (2018) [arXiv:1803.07670] [INSPIRE].
C. Montonen and D.I. Olive, Magnetic Monopoles as Gauge Particles?, Phys. Lett. B 72 (1977) 117 [INSPIRE].
H.A. Buchdahl, Reciprocal Static Metrics and Scalar Fields in the General Theory of Relativity, Phys. Rev. 115 (1959) 1325 [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].
Y.-T. Huang, U. Kol and D. O’Connell, The Double Copy of Electric-Magnetic Duality, arXiv:1911.06318 [INSPIRE].
A.H. Taub, Empty space-times admitting a three parameter group of motions, Annals Math. 53 (1951) 472 [INSPIRE].
E. Newman, L. Tamburino and T. Unti, Empty space generalization of the Schwarzschild metric, J. Math. Phys. 4 (1963) 915 [INSPIRE].
T. Ortin, Gravity and Strings, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2015).
J.F. Plebañski, A class of solutions of Einstein-Maxwell equations, Annals Phys. 90 (1975) 196 [INSPIRE].
Z.W. Chong, G.W. Gibbons, H. Lü and C.N. Pope, Separability and Killing tensors in Kerr-Taub-NUT-de Sitter metrics in higher dimensions, Phys. Lett. B 609 (2005) 124 [hep-th/0405061] [INSPIRE].
F.J. Ernst, New formulation of the axially symmetric gravitational field problem, Phys. Rev. 167 (1968) 1175 [INSPIRE].
J. Ehlers, Transformations of static exterior solutions of Einstein’s gravitational field equations into different solutions by means of conformal mapping, Colloq. Int. CNRS 91 (1962)275 [INSPIRE].
D. Momeni, M. Nouri-Zonoz and R. Ramezani-Arani, MM-NUT disk space via Ehlers transformation, Phys. Rev. D 72 (2005) 064023 [gr-qc/0508036] [INSPIRE].
R.P. Geroch, A Method for generating solutions of Einstein’s equations, J. Math. Phys. 12 (1971) 918 [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].
J.F. Plebanski and M. Demianski, Rotating, charged and uniformly accelerating mass in general relativity, Annals Phys. 98 (1976) 98 [INSPIRE].
J.B. Griffiths and J. Podolsky, A New look at the Plebanski-Demianski family of solutions, Int. J. Mod. Phys. D 15 (2006) 335 [gr-qc/0511091] [INSPIRE].
M. Mars, Space-time Ehlers group: Transformation law for the Weyl tensor, Class. Quant. Grav. 18 (2001) 719 [gr-qc/0101020] [INSPIRE].
M. Mars, T.-T. Paetz and J.M.M. Senovilla, Classification of Kerr-de Sitter-like spacetimes with conformally flat I, Class. Quant. Grav. 34 (2017) 095010 [arXiv:1610.09846] [INSPIRE].
A. G.-P. Gómez-Lobo, Vacuum type D initial data, Class. Quant. Grav. 33 (2016) 175005 [Erratum ibid. 35 (2018) 079501] [arXiv:1602.08075] [INSPIRE].
T.-T. Paetz, Algorithmic characterization results for the Kerr-NUT-(A)dS space-time. I. A space-time approach, J. Math. Phys. 58 (2017) 042501 [arXiv:1701.02959] [INSPIRE].
T.-T. Paetz, Algorithmic characterization results for the Kerr-NUT-(A)dS space-time. II. KIDs for the Kerr-(A)(de Sitter) family, J. Math. Phys. 58 (2017) 042502 [arXiv:1701.03315] [INSPIRE].
V. Frolov, P. Krtous and D. Kubiznak, Black holes, hidden symmetries and complete integrability, Living Rev. Rel. 20 (2017) 6 [arXiv:1705.05482] [INSPIRE].
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Alawadhi, R., Berman, D.S., Spence, B. et al. S-duality and the double copy. J. High Energ. Phys. 2020, 59 (2020). https://doi.org/10.1007/JHEP03(2020)059
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DOI: https://doi.org/10.1007/JHEP03(2020)059