Abstract
Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in \( \mathcal{N} \) = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of \( \mathcal{N} \) = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied \( \mathcal{N} \) = 4 SYM amplitudes via 2D celestial conformal field theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
J. de Boer and S. N. Solodukhin, A Holographic reduction of Minkowski space-time, Nucl. Phys. B 665 (2003) 545 [hep-th/0303006] [INSPIRE].
C. Cheung, A. de la Fuente and R. Sundrum, 4D scattering amplitudes and asymptotic symmetries from 2D CFT, JHEP 01 (2017) 112 [arXiv:1609.00732] [INSPIRE].
S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017) 065022 [arXiv:1705.01027] [INSPIRE].
S. Pasterski, S.-H. Shao and A. Strominger, Gluon Amplitudes as 2d Conformal Correlators, Phys. Rev. D 96 (2017) 085006 [arXiv:1706.03917] [INSPIRE].
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [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].
M. Pate, A.-M. Raclariu and A. Strominger, Conformally Soft Theorem in Gauge Theory, Phys. Rev. D 100 (2019) 085017 [arXiv:1904.10831] [INSPIRE].
D. Nandan, A. Schreiber, A. Volovich and M. Zlotnikov, Celestial Amplitudes: Conformal Partial Waves and Soft Limits, JHEP 10 (2019) 018 [arXiv:1904.10940] [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Celestial amplitudes and conformal soft theorems, Class. Quant. Grav. 36 (2019) 205018 [arXiv:1905.09224] [INSPIRE].
M. Pate, A.-M. Raclariu, A. Strominger and E. Y. Yuan, Celestial Operator Products of Gluons and Gravitons, arXiv:1910.07424 [INSPIRE].
A. Guevara, E. Himwich, M. Pate and A. Strominger, Holographic Symmetry Algebras for Gauge Theory and Gravity, arXiv:2103.03961 [INSPIRE].
N. Arkani-Hamed, M. Pate, A.-M. Raclariu and A. Strominger, Celestial Amplitudes from UV to IR, arXiv:2012.04208 [INSPIRE].
D. Kapec, P. Mitra, A.-M. Raclariu and A. Strominger, 2D Stress Tensor for 4D Gravity, Phys. Rev. Lett. 119 (2017) 121601 [arXiv:1609.00282] [INSPIRE].
E. Crawley, N. Miller, S. A. Narayanan and A. Strominger, State-Operator Correspondence in Celestial Conformal Field Theory, arXiv:2105.00331 [INSPIRE].
S. Pasterski, A. Puhm and E. Trevisani, Celestial Diamonds: Conformal Multiplets in Celestial CFT, arXiv:2105.03516 [INSPIRE].
S. Stieberger and T. R. Taylor, Symmetries of Celestial Amplitudes, Phys. Lett. B 793 (2019) 141 [arXiv:1812.01080] [INSPIRE].
A. Fotopoulos, S. Stieberger, T. R. Taylor and B. Zhu, Extended Super BMS Algebra of Celestial CFT, JHEP 09 (2020) 198 [arXiv:2007.03785] [INSPIRE].
S. Pasterski and A. Puhm, Shifting Spin on the Celestial Sphere, arXiv:2012.15694 [INSPIRE].
A. Brandhuber, G. R. Brown, J. Gowdy, B. Spence and G. Travaglini, Celestial Superamplitudes, arXiv:2105.10263 [INSPIRE].
P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York (1997), [DOI] [INSPIRE].
J.-F. Fortin, K. Intriligator and A. Stergiou, Current OPEs in Superconformal Theories, JHEP 09 (2011) 071 [arXiv:1107.1721] [INSPIRE].
J. M. Henn and J. C. Plefka, Scattering Amplitudes in Gauge Theories, Springer, Berlin Germany (2014) [DOI] [INSPIRE].
A. Schreiber, A. Volovich and M. Zlotnikov, Tree-level gluon amplitudes on the celestial sphere, Phys. Lett. B 781 (2018) 349 [arXiv:1711.08435] [INSPIRE].
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
A. Strominger, Asymptotic Symmetries of Yang-Mills Theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [INSPIRE].
S. Banerjee and S. Ghosh, MHV Gluon Scattering Amplitudes from Celestial Current Algebras, arXiv:2011.00017 [INSPIRE].
H. Elvang, Y.-t. Huang and C. Peng, On-shell superamplitudes in N < 4 SYM, JHEP 09 (2011) 031 [arXiv:1102.4843] [INSPIRE].
E. Casali and A. Puhm, Double Copy for Celestial Amplitudes, Phys. Rev. Lett. 126 (2021) 101602 [arXiv:2007.15027] [INSPIRE].
J. M. Drummond, J. M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N = 4 super Yang-Mills theory, JHEP 05 (2009) 046 [arXiv:0902.2987] [INSPIRE].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
H. A. González, A. Puhm and F. Rojas, Loop corrections to celestial amplitudes, Phys. Rev. D 102 (2020) 126027 [arXiv:2009.07290] [INSPIRE].
A. Brandhuber, G. R. Brown, J. Gowdy, B. Spence and G. Travaglini, Celestial Superamplitudes, to appear.
S. He, Y.-t. Huang and C. Wen, Loop Corrections to Soft Theorems in Gauge Theories and Gravity, JHEP 12 (2014) 115 [arXiv:1405.1410] [INSPIRE].
L. Ferro, T. Łukowski and R. Moerman, From momentum amplituhedron boundaries toamplitude singularities and back, JHEP 07 (2020) 201 [arXiv:2003.13704] [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: 2105.10269
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
Jiang, H. Celestial superamplitude in \( \mathcal{N} \) = 4 SYM theory. J. High Energ. Phys. 2021, 31 (2021). https://doi.org/10.1007/JHEP08(2021)031
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2021)031