Abstract
In celestial holography, four-dimensional scattering amplitudes are considered as two-dimensional conformal correlators of a putative two-dimensional celestial conformal field theory (CCFT). The simplest way of converting momentum space amplitudes into CCFT correlators is by taking their Mellin transforms with respect to light-cone energies. For massless particles, like gluons, however, such a construction leads to three-point and four-point correlators that vanish everywhere except for a measure zero hypersurface of celestial coordinates. This is due to the four-dimensional momentum conservation law that constrains the insertion points of the operators associated with massless particles. These correlators are reminiscent of Coulomb gas correlators that, in the absence of background charges, vanish due to charge conservation. We supply the background momentum by coupling Yang-Mills theory to a background dilaton field, with the (complex) dilaton source localized on the celestial sphere. This picture emerges from the physical interpretation of the solutions of the system of differential equations discovered by Banerjee and Ghosh. We show that the solutions can be written as Mellin transforms of the amplitudes evaluated in such a dilaton background. The resultant three-gluon and four-gluon amplitudes are single-valued functions of celestial coordinates enjoying crossing symmetry and all other properties expected from standard CFT correlators. We use them to extract OPEs and compare them with the OPEs extracted from multi-gluon celestial amplitudes without a dilaton background. We perform the conformal block decomposition of the four-gluon single-valued correlator and determine the dimensions, spin and group representations of the entire primary field spectrum of the Yang-Mills sector of CCFT.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, Princeton University Press, Princeton, NJ, U.S.A. (2018) [arXiv:1703.05448] [INSPIRE].
A.-M. Raclariu, Lectures on Celestial Holography, arXiv:2107.02075 [INSPIRE].
S. Pasterski, Lectures on celestial amplitudes, Eur. Phys. J. C 81 (2021) 1062 [arXiv:2108.04801] [INSPIRE].
P. Di Francesco, P. Mathieu and D. Sénéchal, Conformal Field Theory, Springer, Berlin, Germany (1997).
V. Dotsenko, Série de Cours sur la Théorie Conforme, cel-00092929 (2006).
S. Pasterski, S.-H. Shao and A. Strominger, Gluon Amplitudes as 2d Conformal Correlators, Phys. Rev. D 96 (2017) 085006 [arXiv:1706.03917] [INSPIRE].
S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017) 065022 [arXiv:1705.01027] [INSPIRE].
S. Banerjee and S. Ghosh, MHV gluon scattering amplitudes from celestial current algebras, JHEP 10 (2021) 111 [arXiv:2011.00017] [INSPIRE].
W. Fan, A. Fotopoulos, S. Stieberger, T.R. Taylor and B. Zhu, Conformal blocks from celestial gluon amplitudes. Part II. Single-valued correlators, JHEP 11 (2021) 179 [arXiv:2108.10337] [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, A. Strominger and E.Y. Yuan, Celestial operator products of gluons and gravitons, Rev. Math. Phys. 33 (2021) 2140003 [arXiv:1910.07424] [INSPIRE].
W. Fan, A. Fotopoulos, S. Stieberger, T.R. Taylor and B. Zhu, Conformal blocks from celestial gluon amplitudes, JHEP 05 (2021) 170 [arXiv:2103.04420] [INSPIRE].
T.R. Taylor, A Course in Amplitudes, Phys. Rept. 691 (2017) 1 [arXiv:1703.05670] [INSPIRE].
Y. Hu, L. Ren, A.Y. Srikant and A. Volovich, Celestial dual superconformal symmetry, MHV amplitudes and differential equations, JHEP 12 (2021) 171 [arXiv:2106.16111] [INSPIRE].
S. Stieberger and T.R. Taylor, Symmetries of Celestial Amplitudes, Phys. Lett. B 793 (2019) 141 [arXiv:1812.01080] [INSPIRE].
A. Atanasov, A. Ball, W. Melton, A.-M. Raclariu and A. Strominger, (2, 2) Scattering and the celestial torus, JHEP 07 (2021) 083 [arXiv:2101.09591] [INSPIRE].
M. Ademollo et al., Soft Dilations and Scale Renormalization in Dual Theories, Nucl. Phys. B 94 (1975) 221 [INSPIRE].
J.A. Shapiro, On the Renormalization of Dual Models, Phys. Rev. D 11 (1975) 2937 [INSPIRE].
S. Stieberger and T.R. Taylor, New relations for Einstein-Yang-Mills amplitudes, Nucl. Phys. B 913 (2016) 151 [arXiv:1606.09616] [INSPIRE].
L.J. Dixon, E.W.N. Glover and V.V. Khoze, MHV rules for Higgs plus multi-gluon amplitudes, JHEP 12 (2004) 015 [hep-th/0411092] [INSPIRE].
S.J. Parke and T.R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].
W. Fan, A. Fotopoulos, S. Stieberger, T.R. Taylor and B. Zhu, Celestial Yang-Mills Amplitudes and D = 4 Conformal Blocks, arXiv:2206.08979 [INSPIRE].
F.A. Dolan and H. Osborn, Conformal Partial Waves: Further Mathematical Results, arXiv:1108.6194 [INSPIRE].
H. Osborn, Conformal Blocks for Arbitrary Spins in Two Dimensions, Phys. Lett. B 718 (2012) 169 [arXiv:1205.1941] [INSPIRE].
S. Ferrara, A.F. Grillo, G. Parisi and R. Gatto, Covariant expansion of the conformal four-point function, Nucl. Phys. B 49 (1972) 77 [Erratum ibid. 53 (1973) 643] [INSPIRE].
S. Ferrara, A.F. Grillo, G. Parisi and R. Gatto, The shadow operator formalism for conformal algebra. Vacuum expectation values and operator products, Lett. Nuovo Cim. 4 (1972) 115 [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: 2202.08288
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
Fan, W., Fotopoulos, A., Stieberger, S. et al. Elements of celestial conformal field theory. J. High Energ. Phys. 2022, 213 (2022). https://doi.org/10.1007/JHEP08(2022)213
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)213