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Convolutional double copy in (Anti) de Sitter space

Published 24 Nov 2023 in hep-th and gr-qc | (2311.14319v1)

Abstract: The double copy is a remarkable relationship between gauge theory and gravity that has been explored in a number of contexts, most notably scattering amplitudes and classical solutions. The convolutional double copy provides a straightforward method to bridge the two theories via a precise map for the fields and symmetries at the linearised level. This method has been thoroughly investigated in flat space, offering a comprehensive dictionary both with and without fixing the gauge degrees of freedom. In this paper, we extend this to curved space with an (anti) de Sitter background metric. We work in the temporal gauge, and employ a modified convolution that involves the Mellin transformation in the time direction. As an example, we show that the point-like charge in gauge theory double copies to the (dS-) Schwarzschild black hole solution.

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References (74)
  1. Tim Adamo, John Joseph M. Carrasco, Mariana Carrillo-González, Marco Chiodaroli, Henriette Elvang, Henrik Johansson, Donal O’Connell, Radu Roiban,  and Oliver Schlotterer, “Snowmass White Paper: the Double Copy and its Applications,” in Snowmass 2021 (2022) arXiv:2204.06547 [hep-th] .
  2. Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson,  and Radu Roiban, “The Duality Between Color and Kinematics and its Applications,”  (2019), arXiv:1909.01358 [hep-th] .
  3. Zvi Bern, Tristan Dennen, Yu-tin Huang,  and Michael Kiermaier, “Gravity as the Square of Gauge Theory,” Phys. Rev. D 82, 065003 (2010a), arXiv:1004.0693 [hep-th] .
  4. Zvi Bern, John Joseph M. Carrasco,  and Henrik Johansson, “Perturbative Quantum Gravity as a Double Copy of Gauge Theory,” Phys. Rev. Lett. 105, 061602 (2010b), arXiv:1004.0476 [hep-th] .
  5. Z. Bern, J. J. M. Carrasco,  and Henrik Johansson, “New Relations for Gauge-Theory Amplitudes,” Phys. Rev. D 78, 085011 (2008), arXiv:0805.3993 [hep-ph] .
  6. H. Kawai, D. C. Lewellen,  and S. H. H. Tye, “A Relation Between Tree Amplitudes of Closed and Open Strings,” Nucl. Phys. B 269, 1–23 (1986).
  7. Shanzhong Han, “The Weyl double copy in vacuum spacetimes with a cosmological constant,” JHEP 09, 238 (2022), arXiv:2205.08654 [gr-qc] .
  8. Gokhan Alkac, Mehmet Kemal Gumus,  and Mustafa Tek, “The Kerr-Schild Double Copy in Lifshitz Spacetime,” JHEP 05, 214 (2021), arXiv:2103.06986 [hep-th] .
  9. Siddharth G. Prabhu, “The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar,”   (2020), arXiv:2011.06588 [hep-th] .
  10. Nadia Bahjat-Abbas, Andrés Luna,  and Chris D. White, “The Kerr-Schild double copy in curved spacetime,” JHEP 12, 004 (2017), arXiv:1710.01953 [hep-th] .
  11. Mariana Carrillo-González, Riccardo Penco,  and Mark Trodden, “The classical double copy in maximally symmetric spacetimes,” JHEP 04, 028 (2018), arXiv:1711.01296 [hep-th] .
  12. Jiajie Mei, “Amplitude Bootstrap in (Anti) de Sitter Space And The Four-Point Graviton from Double Copy,”   (2023), arXiv:2305.13894 [hep-th] .
  13. Connor Armstrong, Arthur E. Lipstein,  and Jiajie Mei, “Color/kinematics duality in AdS44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT,” JHEP 02, 194 (2021), arXiv:2012.02059 [hep-th] .
  14. Soner Albayrak, Savan Kharel,  and David Meltzer, “On duality of color and kinematics in (A)dS momentum space,” JHEP 03, 249 (2021), arXiv:2012.10460 [hep-th] .
  15. Luis F. Alday, Connor Behan, Pietro Ferrero,  and Xinan Zhou, “Gluon Scattering in AdS from CFT,” JHEP 06, 020 (2021), arXiv:2103.15830 [hep-th] .
  16. Pranav Diwakar, Aidan Herderschee, Radu Roiban,  and Fei Teng, “BCJ amplitude relations for Anti-de Sitter boundary correlators in embedding space,” JHEP 10, 141 (2021), arXiv:2106.10822 [hep-th] .
  17. Allic Sivaramakrishnan, “Towards color-kinematics duality in generic spacetimes,” JHEP 04, 036 (2022), arXiv:2110.15356 [hep-th] .
  18. Clifford Cheung, Julio Parra-Martinez,  and Allic Sivaramakrishnan, “On-shell correlators and color-kinematics duality in curved symmetric spacetimes,” JHEP 05, 027 (2022), arXiv:2201.05147 [hep-th] .
  19. Aidan Herderschee, Radu Roiban,  and Fei Teng, “On the differential representation and color-kinematics duality of AdS boundary correlators,” JHEP 05, 026 (2022), arXiv:2201.05067 [hep-th] .
  20. J. M. Drummond, R. Glew,  and M. Santagata, “Bern-Carrasco-Johansson relations in AdS5×S3 and the double-trace spectrum of super gluons,” Phys. Rev. D 107, L081901 (2023), arXiv:2202.09837 [hep-th] .
  21. Joseph A. Farrow, Arthur E. Lipstein,  and Paul McFadden, “Double copy structure of CFT correlators,” JHEP 02, 130 (2019), arXiv:1812.11129 [hep-th] .
  22. Arthur E. Lipstein and Paul McFadden, “Double copy structure and the flat space limit of conformal correlators in even dimensions,” Phys. Rev. D 101, 125006 (2020), arXiv:1912.10046 [hep-th] .
  23. Sachin Jain, Renjan Rajan John, Abhishek Mehta, Amin A. Nizami,  and Adithya Suresh, “Double copy structure of parity-violating CFT correlators,” JHEP 07, 033 (2021), arXiv:2104.12803 [hep-th] .
  24. Xinan Zhou, “Double Copy Relation in AdS Space,” Phys. Rev. Lett. 127, 141601 (2021), arXiv:2106.07651 [hep-th] .
  25. Connor Armstrong, Humberto Gomez, Renann Lipinski Jusinskas, Arthur Lipstein,  and Jiajie Mei, “Effective field theories and cosmological scattering equations,” JHEP 08, 054 (2022), arXiv:2204.08931 [hep-th] .
  26. Arthur Lipstein and Silvia Nagy, “Self-dual gravity and color/kinematics duality in AdS44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT,”   (2023), arXiv:2304.07141 [hep-th] .
  27. A. Anastasiou, L. Borsten, M. J. Duff, S. Nagy,  and M. Zoccali, “Gravity as Gauge Theory Squared: A Ghost Story,” Phys. Rev. Lett. 121, 211601 (2018), arXiv:1807.02486 [hep-th] .
  28. Mahdi Godazgar, C. N. Pope, A. Saha,  and Haoyu Zhang, “BRST symmetry and the convolutional double copy,” JHEP 11, 038 (2022), arXiv:2208.06903 [hep-th] .
  29. M. Beneke, P. Hager,  and A. F. Sanfilippo, “Double copy for Lagrangians at trilinear order,” JHEP 02, 083 (2022), arXiv:2106.09054 [hep-th] .
  30. Pietro Ferrero and Dario Francia, “On the Lagrangian formulation of the double copy to cubic order,” JHEP 02, 213 (2021), arXiv:2012.00713 [hep-th] .
  31. L. Borsten, I. Jubb, V. Makwana,  and S. Nagy, “Gauge × gauge = gravity on homogeneous spaces using tensor convolutions,” JHEP 06, 117 (2021), arXiv:2104.01135 [hep-th] .
  32. L. Borsten and S. Nagy, “The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order,” JHEP 07, 093 (2020), arXiv:2004.14945 [hep-th] .
  33. L. Borsten, I. Jubb, V. Makwana,  and S. Nagy, “Gauge × gauge on spheres,” JHEP 06, 096 (2020), arXiv:1911.12324 [hep-th] .
  34. Gabriel Lopes Cardoso, Gianluca Inverso, Silvia Nagy,  and Suresh Nampuri, “Comments on the double copy construction for gravitational theories,” PoS CORFU2017, 177 (2018), arXiv:1803.07670 [hep-th] .
  35. Gabriel Cardoso, Silvia Nagy,  and Suresh Nampuri, “Multi-centered 𝒩=2𝒩2\mathcal{N}=2caligraphic_N = 2 BPS black holes: a double copy description,” JHEP 04, 037 (2017), arXiv:1611.04409 [hep-th] .
  36. G. L. Cardoso, S. Nagy,  and Suresh Nampuri, “A double copy for 𝒩=2𝒩2\mathcal{N}=2caligraphic_N = 2 supergravity: a linearised tale told on-shell,” JHEP 10, 127 (2016), arXiv:1609.05022 [hep-th] .
  37. Ricardo Monteiro, Donal O’Connell,  and Chris D. White, “Black holes and the double copy,” JHEP 12, 056 (2014), arXiv:1410.0239 [hep-th] .
  38. Andrés Luna, Ricardo Monteiro, Isobel Nicholson,  and Donal O’Connell, “Type D Spacetimes and the Weyl Double Copy,” Class. Quant. Grav. 36, 065003 (2019), arXiv:1810.08183 [hep-th] .
  39. Ricardo Monteiro, Donal O’Connell, David Peinador Veiga,  and Matteo Sergola, “Classical solutions and their double copy in split signature,” JHEP 05, 268 (2021), arXiv:2012.11190 [hep-th] .
  40. Ricardo Monteiro, Silvia Nagy, Donal O’Connell, David Peinador Veiga,  and Matteo Sergola, “NS-NS spacetimes from amplitudes,” JHEP 06, 021 (2022), arXiv:2112.08336 [hep-th] .
  41. Andres Luna, Nathan Moynihan,  and Chris D. White, “Why is the Weyl double copy local in position space?” JHEP 12, 046 (2022), arXiv:2208.08548 [hep-th] .
  42. Charlotte Sleight and Massimo Taronna, “Bootstrapping Inflationary Correlators in Mellin Space,” JHEP 02, 098 (2020), arXiv:1907.01143 [hep-th] .
  43. Charlotte Sleight, “A Mellin Space Approach to Cosmological Correlators,” JHEP 01, 090 (2020), arXiv:1906.12302 [hep-th] .
  44. Charlotte Sleight and Massimo Taronna, “From AdS to dS exchanges: Spectral representation, Mellin amplitudes, and crossing,” Phys. Rev. D 104, L081902 (2021a), arXiv:2007.09993 [hep-th] .
  45. Charlotte Sleight and Massimo Taronna, “From dS to AdS and back,” JHEP 12, 074 (2021b), arXiv:2109.02725 [hep-th] .
  46. Charlotte Sleight and Massimo Taronna, “On the consistency of (partially-)massless matter couplings in de Sitter space,” JHEP 10, 156 (2021c), arXiv:2106.00366 [hep-th] .
  47. Juan Martin Maldacena, “The Large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2, 231–252 (1998), arXiv:hep-th/9711200 .
  48. S. S. Gubser, Igor R. Klebanov,  and Alexander M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428, 105–114 (1998), arXiv:hep-th/9802109 .
  49. Edward Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2, 253–291 (1998), arXiv:hep-th/9802150 .
  50. Gerhard Mack, “D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes,”  (2009), arXiv:0907.2407 [hep-th] .
  51. Joao Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,” JHEP 03, 025 (2011), arXiv:1011.1485 [hep-th] .
  52. Miguel F. Paulos, “Towards Feynman rules for Mellin amplitudes,” JHEP 10, 074 (2011), arXiv:1107.1504 [hep-th] .
  53. Simone Giombi, Charlotte Sleight,  and Massimo Taronna, “Spinning AdS Loop Diagrams: Two Point Functions,” JHEP 06, 030 (2018), arXiv:1708.08404 [hep-th] .
  54. Charlotte Sleight and Massimo Taronna, “Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications,” Fortsch. Phys. 66, 1800038 (2018), arXiv:1804.09334 [hep-th] .
  55. George Leibbrandt, “Introduction to noncovariant gauges,” Rev. Mod. Phys. 59, 1067–1119 (1987a).
  56. H. Weyl, The Theory of Groups and Quantum Mechanics, Dover Books on Mathematics (Dover Publications, 1950).
  57. V. Pervushin and T. Tovmasian, “The Heisenberg-Pauli quantization of gravity,” in International Workshop on Symmetry Methods in Physics (1993).
  58. Chung-Pei Ma and Edmund Bertschinger, “Cosmological perturbation theory in the synchronous and conformal Newtonian gauges,” Astrophys. J. 455, 7–25 (1995), arXiv:astro-ph/9506072 .
  59. E. Lifshitz, “Republication of: On the gravitational stability of the expanding universe,” J. Phys. (USSR) 10, 116 (1946).
  60. George Leibbrandt and Su-Long Nyeo, “Application of Unifying Prescription for Axial Type Gauges in QCD,” Phys. Rev. D 39, 1752 (1989).
  61. F. Palumbo, “Exact Evaluation of the Faddeev-popov Determinant in a Complete Axial Gauge on a Torus,” Phys. Lett. B 243, 109–115 (1990).
  62. P. V. Landshoff and P. van Nieuwenhuizen, “Canonical quantization in n.A=0 gauges,” Phys. Rev. D 50, 4157–4161 (1994), arXiv:hep-th/9307117 .
  63. George Leibbrandt and Mark Staley, “Finite temperature calculations in the temporal gauge,” Nucl. Phys. B 428, 469–484 (1994).
  64. Satish D. Joglekar and A. Misra, “Wilson loop and the treatment of axial gauge poles,” Mod. Phys. Lett. A 15, 541–546 (2000a), [Erratum: Mod.Phys.Lett.A 15, 1539 (2000)], arXiv:hep-th/9912020 .
  65. Satish D. Joglekar and A. Misra, “Correct treatment of 1/( eta x k)**p singularities in the axial gauge propagator,” Int. J. Mod. Phys. A 15, 1453–1480 (2000b), [Erratum: Int.J.Mod.Phys.A 15, 3899 (2000)], arXiv:hep-th/9909123 .
  66. Bruno Scheihing-Hitschfeld and Xiaojun Yao, “Gauge Invariance of Non-Abelian Field Strength Correlators: The Axial Gauge Puzzle,” Phys. Rev. Lett. 130, 052302 (2023), arXiv:2205.04477 [hep-ph] .
  67. George Leibbrandt, “Introduction to Noncovariant Gauges,” Rev. Mod. Phys. 59, 1067 (1987b).
  68. G. W. R. Leibbrandt, ‘‘Noncovariant gauges: Quantization of yang-mills and chern-simons theory in axial-type gauges,”  (1994).
  69. J. W. Dyson, “The mathematical theory of relativity. by a. s. eddington. 2nd edition. pp. ix 270. 20s. net. 1924. (cam. univ. press.),” The Mathematical Gazette 12, 351–352 (1925).
  70. Leron Borsten, Branislav Jurco, Hyungrok Kim, Tommaso Macrelli, Christian Saemann,  and Martin Wolf, “Double Copy from Tensor Products of Metric BV■■{}^{\blacksquare}start_FLOATSUPERSCRIPT ■ end_FLOATSUPERSCRIPT-algebras,”   (2023), arXiv:2307.02563 [hep-th] .
  71. G. C. McVittie, “The mass-particle in an expanding universe,”  93, 325–339 (1933).
  72. Miguel Campiglia and Silvia Nagy, “A double copy for asymptotic symmetries in the self-dual sector,” JHEP 03, 262 (2021), arXiv:2102.01680 [hep-th] .
  73. Tim Adamo and Uri Kol, “Classical double copy at null infinity,” Class. Quant. Grav. 39, 105007 (2022), arXiv:2109.07832 [hep-th] .
  74. Vladimir A. Smirnov, Analytic tools for Feynman integrals, Vol. 250 (2012).
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Authors (2)

  1. Qiuyue Liang 
  2. Silvia Nagy 

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