Abstract
We give a new formula for all tree-level correlators of boundary field insertions in gauged \( \mathcal{N}=8 \) supergravity in AdS4; this is an analogue of the tree-level S-matrix in anti-de Sitter space. The formula is written in terms of rational maps from the Riemann sphere to twistor space, with no reference to bulk perturbation theory. It is polynomial in the cosmological constant, and equal to the classical scattering amplitudes of supergravity in the flat space limit. The formula is manifestly supersymmetric, independent of gauge choices on twistor space, and equivalent to expressions computed via perturbation theory at 3-point \( \overline{\mathrm{MHV}} \) and n-point MHV. We also show that the formula factorizes and obeys BCFW recursion in twistor space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
D.B. Fairlie and D.E. Roberts, Dual models without tachyons — A new approach, Durham Preprint PRINT-72-2440 (1972).
D.B. Fairlie, A coding of real null four-momenta into world-sheet co-ordinates, Adv. Math. Phys. 2009 (2009) 284689 [arXiv:0805.2263] [INSPIRE].
D.J. Gross and P.F. Mende, The high-energy behavior of string scattering amplitudes, Phys. Lett. B 197 (1987) 129 [INSPIRE].
D.J. Gross and P.F. Mende, String theory beyond the Planck scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE].
F. Cachazo and D. Skinner, Gravity from rational curves in twistor space, Phys. Rev. Lett. 110 (2013) 161301 [arXiv:1207.0741] [INSPIRE].
R. Roiban, M. Spradlin and A. Volovich, On the tree level S matrix of Yang-Mills theory, Phys. Rev. D 70 (2004) 026009 [hep-th/0403190] [INSPIRE].
T. Adamo, E. Casali, K.A. Roehrig and D. Skinner, On tree amplitudes of supersymmetric Einstein-Yang-Mills theory, arXiv:1507.02207 [INSPIRE].
R. Penrose and W. Rindler, Spinors and space-time, volume 2, Cambridge University Press, Cambridge U.K. (1986).
R.S. Ward and R.O. Wells, Twistor geometry and field theory, Cambridge University Press, Cambridge U.K. (1990).
T. Adamo, Twistor actions for gauge theory and gravity, Ph.D. thesis, University of Oxford, Oxford U.K. (2013), arXiv:1308.2820.
E. Witten, Parity invariance for strings in twistor space, Adv. Theor. Math. Phys. 8 (2004) 779 [hep-th/0403199] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
L. Susskind, Holography in the flat space limit, hep-th/9901079 [INSPIRE].
J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].
S.B. Giddings, The boundary S matrix and the AdS to CFT dictionary, Phys. Rev. Lett. 83 (1999) 2707 [hep-th/9903048] [INSPIRE].
S.B. Giddings, Flat space scattering and bulk locality in the AdS/CFT correspondence, Phys. Rev. D 61 (2000) 106008 [hep-th/9907129] [INSPIRE].
E. Witten, Quantum gravity in de Sitter space, hep-th/0106109 [INSPIRE].
A. Strominger, The dS/CFT correspondence, JHEP 10 (2001) 034 [hep-th/0106113] [INSPIRE].
J.M. Maldacena, Non-gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [INSPIRE].
J.M. Maldacena and G.L. Pimentel, On graviton non-gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
A.L. 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].
M.F. Paulos, Towards Feynman rules for Mellin amplitudes, JHEP 10 (2011) 074 [arXiv:1107.1504] [INSPIRE].
D. Nandan, A. Volovich and C. Wen, On Feynman rules for Mellin amplitudes in AdS/CFT, JHEP 05 (2012) 129 [arXiv:1112.0305] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Unitarity and the holographic S-matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].
V. Gonçalves, J. Penedones and E. Trevisani, Factorization of Mellin amplitudes, JHEP 10 (2015) 040 [arXiv:1410.4185] [INSPIRE].
S. Raju, BCFW for Witten diagrams, Phys. Rev. Lett. 106 (2011) 091601 [arXiv:1011.0780] [INSPIRE].
S. Raju, Recursion relations for AdS/CFT correlators, Phys. Rev. D 83 (2011) 126002 [arXiv:1102.4724] [INSPIRE].
S. Raju, New recursion relations and a flat space limit for AdS/CFT correlators, Phys. Rev. D 85 (2012) 126009 [arXiv:1201.6449] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
P. Benincasa, C. Boucher-Veronneau and F. Cachazo, Taming tree amplitudes in general relativity, JHEP 11 (2007) 057 [hep-th/0702032] [INSPIRE].
S. Raju, Four point functions of the stress tensor and conserved currents in AdS 4 /CFT 3, Phys. Rev. D 85 (2012) 126008 [arXiv:1201.6452] [INSPIRE].
E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Witten diagrams revisited: the AdS geometry of conformal blocks, arXiv:1508.00501 [INSPIRE].
L.J. Mason and D. Skinner, Scattering amplitudes and BCFW recursion in twistor space, JHEP 01 (2010) 064 [arXiv:0903.2083] [INSPIRE].
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, The S-matrix in twistor space, JHEP 03 (2010) 110 [arXiv:0903.2110] [INSPIRE].
T. Adamo, M. Bullimore, L. Mason and D. Skinner, Scattering amplitudes and Wilson loops in twistor space, J. Phys. A 44 (2011) 454008 [arXiv:1104.2890] [INSPIRE].
R. Penrose, Nonlinear gravitons and curved twistor theory, Gen. Rel. Grav. 7 (1976) 31 [INSPIRE].
R.S. Ward, Self-dual space-times with cosmological constant, Commun. Math. Phys. 78 (1980) 1.
M. Wolf, Self-dual supergravity and twistor theory, Class. Quant. Grav. 24 (2007) 6287 [arXiv:0705.1422] [INSPIRE].
R. Penrose, Solutions of the zero-rest-mass equations, J. Math. Phys. 10 (1969) 38 [INSPIRE].
M.G. Eastwood, R. Penrose and R.O. Wells, Cohomology and massless fields, Commun. Math. Phys. 78 (1981) 305.
L.J. Mason and M. Wolf, Twistor actions for self-dual supergravities, Commun. Math. Phys. 288 (2009) 97 [arXiv:0706.1941] [INSPIRE].
L.J. Mason, Twistor actions for non-self-dual fields: a derivation of twistor-string theory, JHEP 10 (2005) 009 [hep-th/0507269] [INSPIRE].
J. Maldacena, Einstein gravity from conformal gravity, arXiv:1105.5632 [INSPIRE].
T. Adamo and L. Mason, Einstein supergravity amplitudes from twistor-string theory, Class. Quant. Grav. 29 (2012) 145010 [arXiv:1203.1026] [INSPIRE].
T. Adamo and L. Mason, Conformal and Einstein gravity from twistor actions, Class. Quant. Grav. 31 (2014) 045014 [arXiv:1307.5043] [INSPIRE].
F. Cachazo, L. Mason and D. Skinner, Gravity in twistor space and its Grassmannian formulation, SIGMA 10 (2014) 051 [arXiv:1207.4712] [INSPIRE].
N. Arkani-Hamed and J. Kaplan, On tree amplitudes in gauge theory and gravity, JHEP 04 (2008) 076 [arXiv:0801.2385] [INSPIRE].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
N. Berkovits, An alternative string theory in twistor space for N = 4 super Yang-Mills,Phys. Rev. Lett. 93 (2004) 011601 [hep-th/0402045] [INSPIRE].
D. Skinner, Twistor strings for N = 8 supergravity, arXiv:1301.0868 [INSPIRE].
O.T. Engelund and R. Roiban, A twistor string for the ABJ(M) theory, JHEP 06 (2014) 088 [arXiv:1401.6242] [INSPIRE].
M.B. Green, H. Ooguri and J.H. Schwarz, Nondecoupling of maximal supergravity from the superstring, Phys. Rev. Lett. 99 (2007) 041601 [arXiv:0704.0777] [INSPIRE].
L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, JHEP 07 (2014) 048 [arXiv:1311.2564] [INSPIRE].
T. Adamo, E. Casali and D. Skinner, A worldsheet theory for supergravity, JHEP 02 (2015) 116 [arXiv:1409.5656] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1508.02554
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Adamo, T. Gravity with a cosmological constant from rational curves. J. High Energ. Phys. 2015, 98 (2015). https://doi.org/10.1007/JHEP11(2015)098
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)098