Abstract
We study contact four-point amplitudes in the spinor-helicity formalism in anti-de Sitter space. We find that these amplitudes can be brought to an especially simple form, which we call canonical. Next, we classify consistent contact amplitudes by requiring correct transformation properties with respect to the AdS isometry algebra. Finally, we establish a connection between the canonical form of AdS amplitudes and scalar multi-trace conformal primaries in flat space.
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References
L.J. Dixon, Calculating scattering amplitudes efficiently, in QCD and beyond. Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics, TASI-95, Boulder, U.S.A., June 4–30, 1995, pp. 539–584, (1996), SLAC-PUB-7106 [hep-ph/9601359] [INSPIRE].
H. Elvang and Y.-t. Huang, Scattering Amplitudes, arXiv:1308.1697 [INSPIRE].
L.J. Dixon, A brief introduction to modern amplitude methods, in Proceedings, 2012 European School of High-Energy Physics (ESHEP 2012): La Pommeraye, Anjou, France, June 06–19, 2012, pp. 31–67, (2014), DOI [arXiv:1310.5353] [INSPIRE].
B. Nagaraj and D. Ponomarev, Spinor-Helicity Formalism for Massless Fields in AdS4, Phys. Rev. Lett. 122 (2019) 101602 [arXiv:1811.08438] [INSPIRE].
B. Nagaraj and D. Ponomarev, Spinor-helicity formalism for massless fields in AdS4. Part II. Potentials, JHEP 06 (2020) 068 [arXiv:1912.07494] [INSPIRE].
T. Adamo and L. Mason, Einstein supergravity amplitudes from twistor-string theory, Class. Quant. Grav. 29 (2012) 145010 [arXiv:1203.1026] [INSPIRE].
D. Skinner, Twistor strings for \( \mathcal{N} \) = 8 supergravity, JHEP 04 (2020) 047 [arXiv:1301.0868] [INSPIRE].
J.M. Maldacena and G.L. Pimentel, On graviton non-Gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].
R.J. Eden, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, The Analytic S-Matrix, Cambridge University Press (1966), [INSPIRE].
H. Liu and A.A. Tseytlin, On four point functions in the CFT/AdS correspondence, Phys. Rev. D 59 (1999) 086002 [hep-th/9807097] [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Comments on 4 point functions in the CFT/AdS correspondence, Phys. Lett. B 452 (1999) 61 [hep-th/9808006] [INSPIRE].
H. Liu, Scattering in anti-de Sitter space and operator product expansion, Phys. Rev. D 60 (1999) 106005 [hep-th/9811152] [INSPIRE].
E. D’Hoker and D.Z. Freedman, General scalar exchange in AdS(d+1), Nucl. Phys. B 550 (1999) 261 [hep-th/9811257] [INSPIRE].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
A. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju and B.C. van Rees, A Natural Language for AdS/CFT Correlators, JHEP 11 (2011) 095 [arXiv:1107.1499] [INSPIRE].
A. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].
A. Fitzpatrick and J. Kaplan, Unitarity and the Holographic S-matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].
O. Aharony, L.F. Alday, A. Bissi and E. Perlmutter, Loops in AdS from Conformal Field Theory, JHEP 07 (2017) 036 [arXiv:1612.03891] [INSPIRE].
S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [INSPIRE].
L.F. Alday and S. Caron-Huot, Gravitational S-matrix from CFT dispersion relations, JHEP 12 (2018) 017 [arXiv:1711.02031] [INSPIRE].
L.F. Alday, A. Bissi and E. Perlmutter, Holographic Reconstruction of AdS Exchanges from Crossing Symmetry, JHEP 08 (2017) 147 [arXiv:1705.02318] [INSPIRE].
E.Y. Yuan, Simplicity in AdS Perturbative Dynamics, arXiv:1801.07283 [INSPIRE].
N. Arkani-Hamed, D. Baumann, H. Lee and G.L. Pimentel, The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities, JHEP 04 (2020) 105 [arXiv:1811.00024] [INSPIRE].
D. Ponomarev, From bulk loops to boundary large-N expansion, JHEP 01 (2020) 154 [arXiv:1908.03974] [INSPIRE].
D. Meltzer, E. Perlmutter and A. Sivaramakrishnan, Unitarity Methods in AdS/CFT, JHEP 03 (2020) 061 [arXiv:1912.09521] [INSPIRE].
L. Rastelli and X. Zhou, Mellin amplitudes for AdS5 × S5, Phys. Rev. Lett. 118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].
L.F. Alday and A. Bissi, Loop Corrections to Supergravity on AdS5 × S5, Phys. Rev. Lett. 119 (2017) 171601 [arXiv:1706.02388] [INSPIRE].
F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Quantum Gravity from Conformal Field Theory, JHEP 01 (2018) 035 [arXiv:1706.02822] [INSPIRE].
X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, in Higher spin gauge theories: Proceedings, 1st Solvay Workshop: Brussels, Belgium, 12–14 May, 2004, pp. 132–197, (2004), [hep-th/0503128] [INSPIRE].
K.I. Bolotin and M.A. Vasiliev, Star product and massless free field dynamics in AdS4, Phys. Lett. B 479 (2000) 421 [hep-th/0001031] [INSPIRE].
N.J. Hitchin, Linear Field Equations on Selfdual Spaces, Proc. Roy. Soc. Lond. A 370 (1980) 173.
M. Plyushchay, D. Sorokin and M. Tsulaia, Higher spins from tensorial charges and OSp(N |2n) symmetry, JHEP 04 (2003) 013 [hep-th/0301067] [INSPIRE].
M. Gary, S.B. Giddings and J. Penedones, Local bulk S-matrix elements and CFT singularities, Phys. Rev. D 80 (2009) 085005 [arXiv:0903.4437] [INSPIRE].
A. Fitzpatrick and J. Kaplan, Scattering States in AdS/CFT, arXiv:1104.2597 [INSPIRE].
C. Fronsdal, Elementary particles in a curved space. ii, Phys. Rev. D 10 (1974) 589 [INSPIRE].
C.R. Graham, R. Jenne, L.J. Mason and G.A.J. Sparling, Conformally Invariant Powers of the Laplacian, I: Existence, J. Lond. Math. Soc. 46 (1992) 557.
X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight, Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory, JHEP 11 (2015) 149 [arXiv:1508.04292] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
S.Y. Li, Y. Wang and S. Zhou, KLT-Like Behaviour of Inflationary Graviton Correlators, JCAP 12 (2018) 023 [arXiv:1806.06242] [INSPIRE].
J.A. Farrow, A.E. Lipstein and P. McFadden, Double copy structure of CFT correlators, JHEP 02 (2019) 130 [arXiv:1812.11129] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering equations and Kawai-Lewellen-Tye orthogonality, Phys. Rev. D 90 (2014) 065001 [arXiv:1306.6575] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions, Phys. Rev. Lett. 113 (2014) 171601 [arXiv:1307.2199] [INSPIRE].
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Nagaraj, B., Ponomarev, D. Spinor-helicity formalism for massless fields in AdS4 III: contact four-point amplitudes. J. High Energ. Phys. 2020, 12 (2020). https://doi.org/10.1007/JHEP08(2020)012
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DOI: https://doi.org/10.1007/JHEP08(2020)012