Abstract
Similar to gravity, an infinite tower of symmetries generated by higher-spin charges has been identified in Yang-Mills theory by studying collinear limits or celestial operator products of gluons. This work aims to recover this loop symmetry in terms of charge aspects constructed on the gluonic Fock space. We propose an explicit construction for these higher spin charge aspects as operators which are polynomial in the gluonic annihilation and creation operators. The core of the paper consists of a proof that the charges we propose form a closed loop algebra to quadratic order. This closure involves using the commutator of the cubic order expansion of the charges with the linear (soft) charge. Quite remarkably, this shows that this infinite-dimensional symmetry constrains the non-linear structure of Yang-Mills theory. We provide a similar all spin proof in gravity for the so-called global quadratic (hard) charges which form the loop wedge subalgebra of w1+∞.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Guevara, E. Himwich, M. Pate and A. Strominger, Holographic symmetry algebras for gauge theory and gravity, JHEP 11 (2021) 152 [arXiv:2103.03961] [INSPIRE].
A. Strominger, w1+∞ Algebra and the Celestial Sphere: Infinite Towers of Soft Graviton, Photon, and Gluon Symmetries, Phys. Rev. Lett. 127 (2021) 221601 [INSPIRE].
E. Himwich, M. Pate and K. Singh, Celestial operator product expansions and w1+∞ symmetry for all spins, JHEP 01 (2022) 080 [arXiv:2108.07763] [INSPIRE].
S. Pasterski, S.-H. Shao and A. Strominger, Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere, Phys. Rev. D 96 (2017) 065026 [arXiv:1701.00049] [INSPIRE].
S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017) 065022 [arXiv:1705.01027] [INSPIRE].
L. Donnay, S. Pasterski and A. Puhm, Asymptotic Symmetries and Celestial CFT, JHEP 09 (2020) 176 [arXiv:2005.08990] [INSPIRE].
L. Freidel, D. Pranzetti and A.-M. Raclariu, Higher spin dynamics in gravity and w1+∞ celestial symmetries, Phys. Rev. D 106 (2022) 086013 [arXiv:2112.15573] [INSPIRE].
L. Freidel and D. Pranzetti, Gravity from symmetry: duality and impulsive waves, JHEP 04 (2022) 125 [arXiv:2109.06342] [INSPIRE].
L. Freidel, R. Oliveri, D. Pranzetti and S. Speziale, The Weyl BMS group and Einstein’s equations, JHEP 07 (2021) 170 [arXiv:2104.05793] [INSPIRE].
E.T. Newman and R. Penrose, New conservation laws for zero rest-mass fields in asymptotically flat space-time, Proc. Roy. Soc. Lond. A 305 (1968) 175 [INSPIRE].
Y. Hu and S. Pasterski, Celestial conformal colliders, JHEP 02 (2023) 243 [arXiv:2211.14287] [INSPIRE].
Y. Hu and S. Pasterski, Detector Operators for Celestial Symmetries, to appear.
T. He, P. Mitra and A. Strominger, 2D Kac-Moody Symmetry of 4D Yang-Mills Theory, JHEP 10 (2016) 137 [arXiv:1503.02663] [INSPIRE].
M. Pate, A.-M. Raclariu and A. Strominger, Color Memory: A Yang-Mills Analog of Gravitational Wave Memory, Phys. Rev. Lett. 119 (2017) 261602 [arXiv:1707.08016] [INSPIRE].
N. Cresto and L. Freidel, Higher spin Symmetry Charges from Yang-Mills theory, to appear.
L. Freidel, D. Pranzetti and A.-M. Raclariu, A discrete basis for celestial holography, arXiv:2212.12469 [INSPIRE].
J. Cotler, N. Miller and A. Strominger, An integer basis for celestial amplitudes, JHEP 08 (2023) 192 [arXiv:2302.04905] [INSPIRE].
I. Halperin and L. Schwartz, Introduction to the Theory of Distributions, University of Toronto Press (2019) [https://doi.org/10.3138/9781442615151].
M. Pate, A.-M. Raclariu, A. Strominger and E.Y. Yuan, Celestial operator products of gluons and gravitons, Rev. Math. Phys. 33 (2021) 2140003 [arXiv:1910.07424] [INSPIRE].
T. Adamo, W. Bu, E. Casali and A. Sharma, Celestial operator products from the worldsheet, JHEP 06 (2022) 052 [arXiv:2111.02279] [INSPIRE].
T. Adamo, W. Bu, E. Casali and A. Sharma, All-order celestial OPE in the MHV sector, JHEP 03 (2023) 252 [arXiv:2211.17124] [INSPIRE].
J.N. Goldberg et al., Spin s spherical harmonics and edth, J. Math. Phys. 8 (1967) 2155 [INSPIRE].
L. Freidel, D. Pranzetti and A.-M. Raclariu, Sub-subleading soft graviton theorem from asymptotic Einstein’s equations, JHEP 05 (2022) 186 [arXiv:2111.15607] [INSPIRE].
W. Fan, A. Fotopoulos and T.R. Taylor, Soft Limits of Yang-Mills Amplitudes and Conformal Correlators, JHEP 05 (2019) 121 [arXiv:1903.01676] [INSPIRE].
A. Guevara, Celestial OPE blocks, arXiv:2108.12706 [INSPIRE].
A. Ashtekar and R.O. Hansen, A unified treatment of null and spatial infinity in general relativity. I — Universal structure, asymptotic symmetries, and conserved quantities at spatial infinity, J. Math. Phys. 19 (1978) 1542 [INSPIRE].
A. Ashtekar, Asymptotic Quantization of the Gravitational Field, Phys. Rev. Lett. 46 (1981) 573 [INSPIRE].
A. Ashtekar, M. Campiglia and A. Laddha, Null infinity, the BMS group and infrared issues, Gen. Rel. Grav. 50 (2018) 140 [arXiv:1808.07093] [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Celestial w1+∞ Symmetries from Twistor Space, SIGMA 18 (2022) 016 [arXiv:2110.06066] [INSPIRE].
V.G. Drinfeld and V.V. Sokolov, Lie algebras and equations of Korteweg-de Vries type, J. Sov. Math. 30 (1984) 1975 [INSPIRE].
G. Compère, R. Oliveri and A. Seraj, Metric reconstruction from celestial multipoles, JHEP 11 (2022) 001 [arXiv:2206.12597] [INSPIRE].
L. Blanchet et al., Multipole expansion of gravitational waves: memory effects and Bondi aspects, JHEP 07 (2023) 123 [arXiv:2303.07732] [INSPIRE].
Acknowledgments
We would like to thank Sabrina Pasterski and Yangrui Hu for many discussions. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. D.P. has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 841923. A.R. is supported by the Heising-Simons Foundation “Observational Signatures of Quantum Gravity” collaboration grant 2021-2817 and acknowledges Perimeter Institute for hospitality while this work was completed.
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: 2306.02373
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
Freidel, L., Pranzetti, D. & Raclariu, AM. On infinite symmetry algebras in Yang-Mills theory. J. High Energ. Phys. 2023, 9 (2023). https://doi.org/10.1007/JHEP12(2023)009
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2023)009