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Homotopy kinematic algebras at null infinity

Felipe Díaz-Jaramillo1,*, Silvia Nagy2,†, and Giorgio Pizzolo2,‡

  • *Contact author: felipe.diaz-jaramillo@hu-berlin.de
  • †Contact author: silvia.nagy@durham.ac.uk
  • ‡Contact author: giorgio.pizzolo@durham.ac.uk
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Phys. Rev. D 112, 086002 – Published 7 October, 2025

DOI: https://doi.org/10.1103/p945-xjlk

Abstract

We present the first formulation of a homotopy algebra adapted to a 1/r expansion near future null infinity (I+). Focusing on self-dual Yang-Mills theory in Bondi coordinates, we demonstrate that imposing the homotopy algebra relations naturally yields the physically consistent fall-off behavior of the fields near I+. Furthermore, we employ this framework to systematically construct kinematic algebras, uncovering novel infinite families of such algebras that satisfy the Jacobi identity on slices near I+.

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References (116)

  1. J. M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998).
  2. S. Pasterski, M. Pate, and A.-M. Raclariu, Celestial holography, in Snowmass 2021 (2021).
  3. A.-M. Raclariu, Lectures on celestial holography, arXiv:2107.02075.
  4. Z. Bern, J. J. M. Carrasco, and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78, 085011 (2008).
  5. Z. Bern, J. J. M. Carrasco, and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett. 105, 061602 (2010).
  6. R. Monteiro and D. O’Connell, The kinematic algebra from the self-dual sector, J. High Energy Phys. 07 (2011) 007.
  7. J. F. Plebanski, Some solutions of complex Einstein equations, J. Math. Phys. (N.Y.) 16, 2395 (1975).
  8. W. A. Bardeen, Selfdual Yang-Mills theory, integrability and multiparton amplitudes, Prog. Theor. Phys. Suppl. 123, 1 (1996).
  9. G. Chalmers and W. Siegel, The selfdual sector of QCD amplitudes, Phys. Rev. D 54, 7628 (1996).
  10. M. Prasad, A. Sinha, and L.-L. Wang, Nonlocal continuity equations for selfdual SU(N) Yang-Mills fields, Phys. Lett. B 87, 237 (1979).
  11. L. Dolan, Kac-Moody algebras and exact solvability in hadronic physics, Phys. Rep. 109, 1 (1984).
  12. A. Parkes, A cubic action for selfdual Yang-Mills, Phys. Lett. B 286, 265 (1992).
  13. D. Cangemi, Selfduality and maximally helicity violating QCD amplitudes, Int. J. Mod. Phys. A 12, 1215 (1997).
  14. A. Popov, M. Bordemann, and H. Romer, Symmetries, currents and conservation laws of selfdual gravity, Phys. Lett. B 385, 63 (1996).
  15. A. Popov, Selfdual Yang-Mills: Symmetries and moduli space, Rev. Math. Phys. 11, 1091 (1999).
  16. G. Chen, H. Johansson, F. Teng, and T. Wang, On the kinematic algebra for BCJ numerators beyond the MHV sector, J. High Energy Phys. 11 (2019) 055.
  17. G. Chen, H. Johansson, F. Teng, and T. Wang, Next-to-MHV Yang-Mills kinematic algebra, J. High Energy Phys. 10 (2021) 042.
  18. R. Monteiro, R. Stark-Muchão, and S. Wikeley, Anomaly and double copy in quantum self-dual Yang-Mills and gravity, J. High Energy Phys. 09 (2023) 030.
  19. R. Monteiro and D. O’Connell, The kinematic algebras from the scattering equations, J. High Energy Phys. 03 (2014) 110.
  20. G. Elor, K. Farnsworth, M. L. Graesser, and G. Herczeg, The Newman-Penrose map and the classical double copy, J. High Energy Phys. 12 (2020) 121.
  21. K. Armstrong-Williams, C. D. White, and S. Wikeley, Non-perturbative aspects of the self-dual double copy, J. High Energy Phys. 08 (2022) 160.
  22. K. Farnsworth, M. L. Graesser, and G. Herczeg, Twistor space origins of the Newman-Penrose map, SciPost Phys. 13, 099 (2022).
  23. E. Skvortsov and R. Van Dongen, Minimal models of field theories: SDYM and SDGR, J. High Energy Phys. 08 (2022) 083.
  24. M. Campiglia and S. Nagy, A double copy for asymptotic symmetries in the self-dual sector, J. High Energy Phys. 03 (2021) 262.
  25. A. Brandhuber, G. R. Brown, G. Chen, J. Gowdy, G. Travaglini, and C. Wen, Amplitudes, Hopf algebras and the colour-kinematics duality, J. High Energy Phys. 12 (2022) 101.
  26. M. Ben-Shahar, L. Garozzo, and H. Johansson, Lagrangians manifesting color-kinematics duality in the NMHV sector of Yang-Mills, J. High Energy Phys. 08 (2023) 222.
  27. M. Carrillo González, A. Lipstein, and S. Nagy, Self-dual cosmology, J. High Energy Phys. 10 (2024) 183.
  28. D. S. Berman, E. Chacón, A. Luna, and C. D. White, The self-dual classical double copy, and the Eguchi-Hanson instanton, J. High Energy Phys. 01 (2019) 107.
  29. S. Nagy and J. Peraza, Radiative phase space extensions at all orders in r for self-dual Yang-Mills and gravity, J. High Energy Phys. 02 (2023) 202.
  30. R. Monteiro, Celestial chiral algebras, colour-kinematics duality and integrability, J. High Energy Phys. 01 (2023) 092.
  31. K. Krasnov and E. Skvortsov, Flat self-dual gravity, J. High Energy Phys. 08 (2021) 082.
  32. R. Monteiro, From Moyal deformations to chiral higher-spin theories and to celestial algebras, J. High Energy Phys. 03 (2023) 062.
  33. A. Lipstein and S. Nagy, Self-dual gravity and color-kinematics duality in AdS4, Phys. Rev. Lett. 131, 081501 (2023).
  34. L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, and M. Wolf, Double-copying self-dual Yang-Mills theory to self-dual gravity on twistor space, J. High Energy Phys. 11 (2023) 172.
  35. G. R. Brown, J. Gowdy, and B. Spence, Self-dual fields on self-dual backgrounds and the double copy, Phys. Rev. D 109, 026009 (2024).
  36. G. Doran, R. Monteiro, and S. Wikeley, On the anomaly interpretation of amplitudes in self-dual Yang-Mills and gravity, J. High Energy Phys. 07 (2024) 139.
  37. C. Chowdhury, G. Doran, A. Lipstein, R. Monteiro, S. Nagy, and K. Singh, Light-cone actions and correlators of self-dual theories in AdS4, J. High Energy Phys. 01 (2025) 172.
  38. G. Lopes Cardoso, S. Mahapatra, and S. Nagy, Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy, J. High Energy Phys. 10 (2024) 030.
  39. D. H. Correa, C. Lopez-Arcos, and A. Quintero Velez, Tree- and one-loop-level double copy for the (anti)self-dual sectors of Yang-Mills and gravity theories, Phys. Rev. D 111, 065001 (2025).
  40. M. Ben-Shahar and H. Johansson, Off-shell color-kinematics duality for Chern-Simons, J. High Energy Phys. 08 (2022) 035.
  41. L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, and M. Wolf, Kinematic lie algebras from twistor spaces, Phys. Rev. Lett. 131, 041603 (2023).
  42. R. Bonezzi, F. Diaz-Jaramillo, and O. Hohm, Double copy of 3D Chern-Simons theory and 6D Kodaira-Spencer gravity, Phys. Rev. D 110, 045024 (2024).
  43. C. Cheung and C.-H. Shen, Symmetry for flavor-kinematics duality from an action, Phys. Rev. Lett. 118, 121601 (2017).
  44. G. Chen, G. Lin, and C. Wen, Kinematic Hopf algebra for amplitudes and form factors, Phys. Rev. D 107, L081701 (2023).
  45. A. Brandhuber, G. Chen, H. Johansson, G. Travaglini, and C. Wen, Kinematic Hopf algebra for Bern-Carrasco-Johansson numerators in heavy-mass effective field theory and Yang-Mills theory, Phys. Rev. Lett. 128, 121601 (2022).
  46. M. Ben-Shahar and M. Guillen, 10D super-Yang-Mills scattering amplitudes from its pure spinor action, J. High Energy Phys. 12 (2021) 014.
  47. L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, and M. Wolf, Tree-level color-kinematics duality from pure spinor actions, Phys. Rev. D 108, 126012 (2023).
  48. K. Armstrong-Williams, S. Nagy, C. D. White, and S. Wikeley, What can Abelian gauge theories teach us about kinematic algebras?, J. High Energy Phys. 08 (2024) 169.
  49. M. Reiterer, A homotopy BV algebra for Yang-Mills and color-kinematics, arXiv:1912.03110.
  50. R. Bonezzi, C. Chiaffrino, F. Diaz-Jaramillo, and O. Hohm, Gauge invariant double copy of Yang-Mills theory: The quartic theory, Phys. Rev. D 107, 126015 (2023).
  51. R. Bonezzi, F. Diaz-Jaramillo, and O. Hohm, The gauge structure of double field theory follows from Yang-Mills theory, Phys. Rev. D 106, 026004 (2022).
  52. L. Borsten, H. Kim, B. Jurčo, T. Macrelli, C. Saemann, and M. Wolf, Double copy from homotopy algebras, Fortschr. Phys. 69, 2100075 (2021).
  53. L. Borsten, H. Kim, B. Jurčo, T. Macrelli, C. Saemann, and M. Wolf, Tree-level color–kinematics duality implies loop-level color–kinematics duality up to counterterms, Nucl. Phys. B989, 116144 (2023).
  54. L. Borsten, B. Jurčo, H. Kim, T. Macrelli, C. Saemann, and M. Wolf, Becchi-Rouet-Stora-Tyutin-Lagrangian double copy of Yang-Mills theory, Phys. Rev. Lett. 126, 191601 (2021).
  55. R. Bonezzi, C. Chiaffrino, F. Diaz-Jaramillo, and O. Hohm, Weakly constrained double field theory: The quartic theory, arXiv:2306.00609.
  56. V. G. Escudero, C. Lopez-Arcos, and A. Quintero Velez, Homotopy double copy and the Kawai–Lewellen–Tye relations for the non-Abelian and tensor Navier–Stokes equations, J. Math. Phys. (N.Y.) 64, 032304 (2023).
  57. L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, and M. Wolf, Double copy from tensor products of metric BV▪-algebras, Fortschr. Phys. 73, 2300270 (2025).
  58. C. Chiaffrino, T. Ersoy, and O. Hohm, Holography as homotopy, J. High Energy Phys. 09 (2024) 161.
  59. L. Alfonsi, L. Borsten, H. Kim, M. Wolf, and C. A. S. Young, Full S-matrices and Witten diagrams with (relative) L-infinity algebras, J. High Energy Phys. 07 (2025) 267.
  60. A. Strominger, Asymptotic symmetries of Yang-Mills theory, J. High Energy Phys. 07 (2014) 151.
  61. A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448.
  62. R. Bonezzi, F. Diaz-Jaramillo, and S. Nagy, Gauge independent kinematic algebra of self-dual Yang-Mills theory, Phys. Rev. D 108, 065007 (2023).
  63. R. Bonezzi, C. Chiaffrino, F. Diaz-Jaramillo, and O. Hohm, Tree-level scattering amplitudes via homotopy transfer, arXiv:2312.09306.
  64. R. Bonezzi, C. Chiaffrino, F. Diaz-Jaramillo, and O. Hohm, Weakly constrained double field theory as the double copy of Yang-Mills theory, Phys. Rev. D 109, 066020 (2024).
  65. R. Bonezzi, C. Chiaffrino, F. Diaz-Jaramillo, and O. Hohm, Gravity = Yang–Mills, Symmetry 15, 2062 (2023).
  66. S. Nagy, J. Peraza, and G. Pizzolo, Infinite-dimensional hierarchy of recursive extensions for all subn-leading soft effects in Yang-Mills, J. High Energy Phys. 12 (2024) 068.
  67. M. Campiglia and J. Peraza, Charge algebra for non-Abelian large gauge symmetries at O(r), J. High Energy Phys. 12 (2021) 058.
  68. S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140, B516 (1965).
  69. T. He, P. Mitra, A. P. Porfyriadis, and A. Strominger, New symmetries of massless QED, J. High Energy Phys. 10 (2014) 112.
  70. A. S. Arvanitakis, O. Hohm, C. Hull, and V. Lekeu, Homotopy transfer and effective field theory I: Tree-level, Fortschr. Phys. 70, 2200003 (2022).
  71. T. Adamo and U. Kol, Classical double copy at null infinity, Classical Quantum Gravity 39, 105007 (2022).
  72. P. Ferrero, D. Francia, C. Heissenberg, and M. Romoli, Double-copy supertranslations, Phys. Rev. D 110, 026009 (2024).
  73. P. Mao and W. Zhao, Note on the asymptotic structure of Kerr-Schild form, J. High Energy Phys. 01 (2022) 030.
  74. H. Godazgar, M. Godazgar, R. Monteiro, D. Peinador Veiga, and C. N. Pope, Asymptotic Weyl double copy, J. High Energy Phys. 11 (2021) 126.
  75. M. Campiglia and A. Laddha, Asymptotic symmetries of QED and Weinberg’s soft photon theorem, J. High Energy Phys. 07 (2015) 115.
  76. M. Campiglia and J. Peraza, Generalized BMS charge algebra, Phys. Rev. D 101, 104039 (2020).
  77. A. Strominger, On BMS invariance of gravitational scattering, J. High Energy Phys. 07 (2014) 152.
  78. V. Lysov, S. Pasterski, and A. Strominger, Low’s subleading soft theorem as a symmetry of QED, Phys. Rev. Lett. 113, 111601 (2014).
  79. W. Donnelly and L. Freidel, Local subsystems in gauge theory and gravity, J. High Energy Phys. 09 (2016) 102.
  80. A. J. Speranza, Local phase space and edge modes for diffeomorphism-invariant theories, J. High Energy Phys. 02 (2018) 021.
  81. L. Freidel, M. Geiller, and D. Pranzetti, Edge modes of gravity. Part III. Corner simplicity constraints, J. High Energy Phys. 01 (2021) 100.
  82. L. Freidel, M. Geiller, and D. Pranzetti, Edge modes of gravity. Part II. Corner metric and Lorentz charges, J. High Energy Phys. 11 (2020) 027.
  83. L. Freidel, M. Geiller, and D. Pranzetti, Edge modes of gravity. Part I. Corner potentials and charges, J. High Energy Phys. 11 (2020) 026.
  84. L. Freidel, A canonical bracket for open gravitational system, J. High Energy Phys. 11 (2020) 026.
  85. L. Ciambelli, R. G. Leigh, and P.-C. Pai, Embeddings and integrable charges for extended corner symmetry, Phys. Rev. Lett. 128, 171302 (2022).
  86. L. Freidel, R. Oliveri, D. Pranzetti, and S. Speziale, Extended corner symmetry, charge bracket and Einstein’s equations, J. High Energy Phys. 09 (2021) 083.
  87. L. Freidel, D. Pranzetti, and A.-M. Raclariu, Sub-subleading soft graviton theorem from asymptotic Einstein’s equations, J. High Energy Phys. 05 (2022) 186.
  88. L. Ciambelli and R. G. Leigh, Isolated surfaces and symmetries of gravity, Phys. Rev. D 104, 046005 (2021).
  89. S. Nagy, J. Peraza, and G. Pizzolo, A general hierarchy of charges at null infinity via the Todd polynomials, Phys. Rev. D 111, L061903 (2025).
  90. M. Geiller, Celestial w1+∞ charges and the subleading structure of asymptotically-flat spacetimes, SciPost Phys. 18, 023 (2025).
  91. M. Geiller and C. Zwikel, The partial Bondi gauge: Further enlarging the asymptotic structure of gravity, SciPost Phys. 13, 108 (2022).
  92. J. Peraza, Renormalized electric and magnetic charges for O(rn) large gauge symmetries, J. High Energy Phys. 01 (2024) 175.
  93. M. Campiglia and A. Laddha, Asymptotic charges in massless QED revisited: A view from spatial infinity, J. High Energy Phys. 05 (2019) 207.
  94. C. N. Pope, L. J. Romans, and X. Shen, The complete structure of W(Infinity), Phys. Lett. B 236, 173 (1990).
  95. I. Bakas, The Large n limit of extended conformal symmetries, Phys. Lett. B 228, 57 (1989).
  96. D. B. Fairlie and J. Nuyts, Deformations and eenormalizations of W (infinity), Commun. Math. Phys. 134, 413 (1990).
  97. C. N. Pope, Lectures on W algebras and W gravity, in Summer School in High-energy Physics and Cosmology (1991), pp. 827–867.
  98. C. N. Pope, X. Shen, K. W. Xu, and K.-j. Yuan, SL(infinity,R) symmetry of quantum W(infinity) gravity, Nucl. Phys. B376, 52 (1992).
  99. A. Strominger, w1+∞ algebra and the celestial sphere: Infinite towers of soft graviton, photon, and gluon symmetries, Phys. Rev. Lett. 127, 221601 (2021).
  100. A. Guevara, E. Himwich, M. Pate, and A. Strominger, Holographic symmetry algebras for gauge theory and gravity, J. High Energy Phys. 11 (2021) 152.
  101. A. Strominger, w(1+infinity) and the celestial sphere, Phys. Rev. Lett. 127, 221601 (2021).
  102. E. Himwich, M. Pate, and K. Singh, Celestial operator product expansions and w1+∞ symmetry for all spins, J. High Energy Phys. 01 (2022) 080.
  103. H. Jiang, Holographic chiral algebra: Supersymmetry, infinite Ward identities, and EFTs, J. High Energy Phys. 01 (2022) 113.
  104. C. P. Boyer and J. F. Plebanski, An infinite hierarchy of conservation laws and nonlinear superposition principles for self‐dual Einstein spaces, J. Math. Phys. (N.Y.) 26, 229 (1985).
  105. Q.-H. Park, Extended conformal symmetries in real heavens, Phys. Lett. B 236, 429 (1990).
  106. Q.-H. Park, Selfdual gravity as a Large N limit of the two-dimensional nonlinear σ model, Phys. Lett. B 238, 287 (1990).
  107. T. Adamo, L. Mason, and A. Sharma, Celestial w1+∞ symmetries from twistor space, SIGMA 18, 016 (2022).
  108. W. Bu, S. Heuveline, and D. Skinner, Moyal deformations, W1+∞ and celestial holography, J. High Energy Phys. 12 (2022) 011.
  109. R. Bittleston, S. Heuveline, and D. Skinner, The celestial chiral algebra of self-dual gravity on Eguchi-Hanson space, J. High Energy Phys. 09 (2023) 008.
  110. R. Bittleston, G. Bogna, S. Heuveline, A. Kmec, L. Mason, and D. Skinner, On AdS4 deformations of celestial symmetries, J. High Energy Phys. 07 (2024) 010.
  111. T. R. Taylor and B. Zhu, w1+∞ algebra with a cosmological constant and the celestial sphere, Phys. Rev. Lett. 132, 221602 (2024).
  112. A. Kmec, L. Mason, R. Ruzziconi, and A. Yelleshpur Srikant, Celestial Lw1+∞ charges from a twistor action, J. High Energy Phys. 10 (2024) 250.
  113. L. Freidel, D. Pranzetti, and A.-M. Raclariu, Higher spin dynamics in gravity and w1+∞ celestial symmetries, Phys. Rev. D 106, 086013 (2022).
  114. L. Freidel, D. Pranzetti, and A.-M. Raclariu, On infinite symmetry algebras in Yang-Mills theory, J. High Energy Phys. 12 (2023) 009.
  115. Y. Hu and S. Pasterski, Detector operators for celestial symmetries, J. High Energy Phys. 12 (2023) 035.
  116. G. Pizzolo (to be published).

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Phys. Rev. D 112, 086002– Published 7 October, 2025
  • Received 4 June 2025
  • Accepted 18 September 2025
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