Abstract
We discuss the properties of recently constructed “single-valued” celestial four-gluon amplitudes. We show that the amplitude factorizes into the “current” part and the “scalar” part. The current factor is given by the group-dependent part of the Wess-Zumino-Witten correlator of four holomorphic currents with a non-vanishing level of Kač-Moody algebra. The scalar factor can be expressed in terms of a complex integral of the Koba-Nielsen form, similar to the integrals describing four-point correlators in Coulomb gas models and, more generally, in the infinite central charge limit of Liouville theory. The scalar part can be also obtained by a dimensional reduction of a single D = 4 conformal block and the shadow block from Minkowski space to the celestial sphere.
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References
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
S. Stieberger and T.R. Taylor, Symmetries of Celestial Amplitudes, Phys. Lett. B 793 (2019) 141 [arXiv:1812.01080] [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].
S. Pasterski, Lectures on celestial amplitudes, Eur. Phys. J. C 81 (2021) 1062 [arXiv:2108.04801] [INSPIRE].
S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017) 065022 [arXiv:1705.01027] [INSPIRE].
S. Mizera and S. Pasterski, Celestial Geometry, arXiv:2204.02505 [INSPIRE].
W. Fan, A. Fotopoulos, S. Stieberger, T.R. Taylor and B. Zhu, Elements of celestial conformal field theory, JHEP 08 (2022) 213 [arXiv:2202.08288] [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].
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].
P. Di Francesco, P. Mathieu, D. Sénéchal, Conformal Field Theory, Springer (1997) [DOI].
S. Banerjee and S. Ghosh, MHV gluon scattering amplitudes from celestial current algebras, JHEP 10 (2021) 111 [arXiv:2011.00017] [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].
V.S. Dotsenko and V.A. Fateev, Four Point Correlation Functions and the Operator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c < 1, Nucl. Phys. B 251 (1985) 691 [INSPIRE].
V.S. Dotsenko and V.A. Fateev, Conformal Algebra and Multipoint Correlation Functions in Two-Dimensional Statistical Models, Nucl. Phys. B 240 (1984) 312 [INSPIRE].
Vl.S. Dotsenko, Série de Cours sur la Théorie Conforme. Partie I: Théorie Conforme Minimal, (2006).
K. Aomoto and M. Kita, Theory of Hypergeometric Functions, Springer, Tokyo, (2011) [DOI].
Y. Goto and K. Matsumoto, The monodromy representation and twisted period relations for Appell’s hypergeometric function F4, Nagoya Math. J. 217 (2015) 61.
L.J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, U.K. (2008) [ISBN: 9780521090612].
F.A. Dolan and H. Osborn, Implications of N = 1 superconformal symmetry for chiral fields, Nucl. Phys. B 593 (2001) 599 [hep-th/0006098] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [INSPIRE].
D. Simmons-Duffin, Projectors, Shadows, and Conformal Blocks, JHEP 04 (2014) 146 [arXiv:1204.3894] [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].
E. Casali, W. Melton and A. Strominger, Celestial Amplitudes as AdS-Witten Diagrams, arXiv:2204.10249 [INSPIRE].
H. Dorn and H.J. Otto, Two and three point functions in Liouville theory, Nucl. Phys. B 429 (1994) 375 [hep-th/9403141] [INSPIRE].
M. Hogervorst, Dimensional Reduction for Conformal Blocks, JHEP 09 (2016) 017 [arXiv:1604.08913] [INSPIRE].
A. Kaviraj, S. Rychkov and E. Trevisani, Random Field Ising Model and Parisi-Sourlas supersymmetry. Part I. Supersymmetric CFT, JHEP 04 (2020) 090 [arXiv:1912.01617] [INSPIRE].
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Fan, W., Fotopoulos, A., Stieberger, S. et al. Celestial Yang-Mills amplitudes and D = 4 conformal blocks. J. High Energ. Phys. 2022, 182 (2022). https://doi.org/10.1007/JHEP09(2022)182
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DOI: https://doi.org/10.1007/JHEP09(2022)182