Abstract
We consider D-dimensional amplitudes in R2 gravities (conformal gravity in D = 4) and in the recently introduced (DF)2 gauge theory, from the perspective of the CHY formulae and ambitwistor string theory. These theories are related through the BCJ double-copy construction, and the (DF)2 gauge theory obeys color-kinematics duality. We work out the worldsheet details of these theories and show that they admit a formulation as integrals on the support of the scattering equations, or alternatively, as ambitwistor string theories. For gravity, this generalizes the work done by Berkovits and Witten on conformal gravity to D dimensions. The ambitwistor is also interpreted as a D-dimensional generalization of Witten’s twistor string (SYM + conformal supergravity). As part of our ambitwistor investigation, we discover another (DF)2 gauge theory containing a photon that couples to Einstein gravity. This theory can provide an alternative KLT description of Einstein gravity compared to the usual Yang-Mills squared.
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].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, JHEP 07 (2014) 033 [arXiv:1309.0885] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM, JHEP 07 (2015) 149 [arXiv:1412.3479] [INSPIRE].
L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, JHEP 07 (2014) 048 [arXiv:1311.2564] [INSPIRE].
E. Casali, Y. Geyer, L. Mason, R. Monteiro and K.A. Roehrig, New Ambitwistor String Theories, JHEP 11 (2015) 038 [arXiv:1506.08771] [INSPIRE].
H. Johansson and J. Nohle, Conformal Gravity from Gauge Theory, arXiv:1707.02965 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Conformal supergravity, Phys. Rept. 119 (1985) 233 [INSPIRE].
H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
N. Berkovits and E. Witten, Conformal supergravity in twistor-string theory, JHEP 08 (2004) 009 [hep-th/0406051] [INSPIRE].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
J. Maldacena, Einstein Gravity from Conformal Gravity, arXiv:1105.5632 [INSPIRE].
J.J.M. Carrasco, R. Kallosh, R. Roiban and A.A. Tseytlin, On the U(1) duality anomaly and the S-matrix of N = 4 supergravity, JHEP 07 (2013) 029 [arXiv:1303.6219] [INSPIRE].
E.H. Simmons, Dimension-six Gluon Operators as Probes of New Physics, Phys. Lett. B 226 (1989) 132 [INSPIRE].
E.H. Simmons, Higher dimension gluon operators and hadronic scattering, Phys. Lett. B 246 (1990) 471 [INSPIRE].
P.L. Cho and E.H. Simmons, Looking for gluon substructure at the Tevatron, Phys. Lett. B 323 (1994) 401 [hep-ph/9307345] [INSPIRE].
A. Duff and D. Zeppenfeld, Probing QCD via four jet decays of the Z boson, Z. Phys. C 53 (1992) 529 [INSPIRE].
H.K. Dreiner, A. Duff and D. Zeppenfeld, How well do we know the three gluon vertex?, Phys. Lett. B 282 (1992) 441 [INSPIRE].
L.J. Dixon and Y. Shadmi, Testing gluon selfinteractions in three jet events at hadron colliders, Nucl. Phys. B 423 (1994) 3 [Erratum ibid. B 452 (1995) 724] [hep-ph/9312363] [INSPIRE].
L.A. Barreiro and R. Medina, Revisiting the S-matrix approach to the open superstring low energy effective lagrangian, JHEP 10 (2012) 108 [arXiv:1208.6066] [INSPIRE].
L.A. Barreiro and R. Medina, RNS derivation of N-point disk amplitudes from the revisited S-matrix approach, Nucl. Phys. B 886 (2014) 870 [arXiv:1310.5942] [INSPIRE].
R.H. Boels and R. Medina, Graviton and gluon scattering from first principles, Phys. Rev. Lett. 118 (2017) 061602 [arXiv:1607.08246] [INSPIRE].
R. Kleiss and H. Kuijf, Multigluon cross sections and 5-jet production at hadron colliders, Nucl. Phys. B 312 (1989) 616 [INSPIRE].
V. Del Duca, A. Frizzo and F. Maltoni, Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit, Nucl. Phys. B 568 (2000) 211 [hep-ph/9909464] [INSPIRE].
V. Del Duca, L.J. Dixon and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level, Nucl. Phys. B 571 (2000) 51 [hep-ph/9910563] [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].
T. Sondergaard, New Relations for Gauge-Theory Amplitudes with Matter, Nucl. Phys. B 821 (2009) 417 [arXiv:0903.5453] [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Minimal Basis for Gauge Theory Amplitudes, Phys. Rev. Lett. 103 (2009) 161602 [arXiv:0907.1425] [INSPIRE].
B. Feng, R. Huang and Y. Jia, Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program, Phys. Lett. B 695 (2011) 350 [arXiv:1004.3417] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [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].
C.S. Lam and Y.-P. Yao, Evaluation of the Cachazo-He-Yuan gauge amplitude, Phys. Rev. D 93 (2016) 105008 [arXiv:1602.06419] [INSPIRE].
S. He and Y. Zhang, New Formulas for Amplitudes from Higher-Dimensional Operators, JHEP 02 (2017) 019 [arXiv:1608.08448] [INSPIRE].
C. Baadsgaard, N.E.J. Bjerrum-Bohr, J.L. Bourjaily and P.H. Damgaard, Integration Rules for Scattering Equations, JHEP 09 (2015) 129 [arXiv:1506.06137] [INSPIRE].
N.E.J. Bjerrum-Bohr, J.L. Bourjaily, P.H. Damgaard and B. Feng, Analytic representations of Yang-Mills amplitudes, Nucl. Phys. B 913 (2016) 964 [arXiv:1605.06501] [INSPIRE].
K. Zhou, J. Rao and B. Feng, Derivation of Feynman Rules for Higher Order Poles Using Cross-ratio Identities in CHY Construction, JHEP 06 (2017) 091 [arXiv:1705.04783] [INSPIRE].
R. Monteiro and D. O’Connell, The Kinematic Algebras from the Scattering Equations, JHEP 03 (2014) 110 [arXiv:1311.1151] [INSPIRE].
S. Weinzierl, On the solutions of the scattering equations, JHEP 04 (2014) 092 [arXiv:1402.2516] [INSPIRE].
S.G. Naculich, Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles, JHEP 09 (2014) 029 [arXiv:1407.7836] [INSPIRE].
Y.-j. Du, F. Teng and Y.-s. Wu, CHY formula and MHV amplitudes, JHEP 05 (2016) 086 [arXiv:1603.08158] [INSPIRE].
T. Azevedo and R.L. Jusinskas, Connecting the ambitwistor and the sectorized heterotic strings, arXiv:1707.08840 [INSPIRE].
M. de Roo, The R 2 action in D = 10 conformal supergravity, Nucl. Phys. B 372 (1992) 243 [INSPIRE].
E. Bergshoeff, M. de Roo and B. de Wit, Conformal Supergravity in Ten-dimensions, Nucl. Phys. B 217 (1983) 489 [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: 1707.02192
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Azevedo, T., Engelund, O.T. Ambitwistor formulations of R2 gravity and (DF)2 gauge theories. J. High Energ. Phys. 2017, 52 (2017). https://doi.org/10.1007/JHEP11(2017)052
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2017)052