Abstract
We construct entangled states of gluons that scatter exactly as if they were gravitons. Operationally, these objects implement the double copy at the level of the wave function. Our analysis begins with a general ansatz for a wave function characterizing gluons in two copies of SU(N ) gauge theory. Given relatively minimal assumptions following from permutation invariance and dimensional analysis, the three- and four-particle wave functions generate scattering amplitudes that automatically coincide exactly with gravity, modulo normalization. For five-particle scattering the match is not automatic but imposing certain known selection rules on the amplitude is sufficient to uniquely reproduce gravity. The resulting amplitudes exhibit a color-dressed and permutation-invariant form of the usual double copy relations. We compute the entanglement entropy between the two gauge theory copies and learn that these states are maximally-entangled at large N . Moreover, this approach extends immediately to effective field theories, where Born-Infeld photons and Galileons can be similarly recast as entangled gluons and pions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
Z. Bern, J.J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, The Duality Between Color and Kinematics and its Applications, arXiv:1909.01358 [INSPIRE].
Z. Bern, J.J.M. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes, Phys. Rev. D 85 (2012) 105014 [arXiv:1201.5366] [INSPIRE].
Z. Bern et al., Ultraviolet Properties of \( \mathcal{N} \) = 8 Supergravity at Five Loops, Phys. Rev. D 98 (2018) 086021 [arXiv:1804.09311] [INSPIRE].
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M.P. Solon and M. Zeng, Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order, Phys. Rev. Lett. 122 (2019) 201603 [arXiv:1901.04424] [INSPIRE].
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M.P. Solon and M. Zeng, Black Hole Binary Dynamics from the Double Copy and Effective Theory, JHEP 10 (2019) 206 [arXiv:1908.01493] [INSPIRE].
P. Benincasa and F. Cachazo, Consistency Conditions on the S-matrix of Massless Particles, arXiv:0705.4305 [INSPIRE].
H. Elvang and Y.-t. Huang, Scattering Amplitudes, arXiv:1308.1697 [INSPIRE].
C. Cheung, TASI Lectures on Scattering Amplitudes, in proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics: Anticipating the Next Discoveries in Particle Physics (TASI 2016), Boulder, CO, U.S.A., 6 June–1 July 2016, pp. 571–623 [arXiv:1708.03872] [INSPIRE].
G. Chen and Y.-J. Du, Amplitude Relations in Non-linear σ-model, JHEP 01 (2014) 061 [arXiv:1311.1133] [INSPIRE].
J.J.M. Carrasco, C.R. Mafra and O. Schlotterer, Abelian Z-theory: NLSM amplitudes and αd -corrections from the open string, JHEP 06 (2017) 093 [arXiv:1608.02569] [INSPIRE].
C. Cheung and C.-H. Shen, Symmetry for Flavor-Kinematics Duality from an Action, Phys. Rev. Lett. 118 (2017) 121601 [arXiv:1612.00868] [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].
C. Cheung, C.-H. Shen and C. Wen, Unifying Relations for Scattering Amplitudes, JHEP 02 (2018) 095 [arXiv:1705.03025] [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].
L.J. Dixon, Calculating scattering amplitudes efficiently, in QCD and beyond, proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 95), Boulder, CO, U.S.A., 4–30 June 1995, pp. 539–584 [hep-ph/9601359] [INSPIRE].
N. Arkani-Hamed, L. Rodina and J. Trnka, Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance, Phys. Rev. Lett. 120 (2018) 231602 [arXiv:1612.02797] [INSPIRE].
R. Monteiro, D. O’Connell and C.D. White, Black holes and the double copy, JHEP 12 (2014) 056 [arXiv:1410.0239] [INSPIRE].
R. Monteiro, D. O’Connell and C.D. White, Gravity as a double copy of gauge theory: from amplitudes to black holes, Int. J. Mod. Phys. D 24 (2015) 1542008 [INSPIRE].
A. Luna et al., Perturbative spacetimes from Yang-Mills theory, JHEP 04 (2017) 069 [arXiv:1611.07508] [INSPIRE].
Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory, Phys. Rev. D 82 (2010) 065003 [arXiv:1004.0693] [INSPIRE].
R. Monteiro and D. O’Connell, The Kinematic Algebra From the Self-Dual Sector, JHEP 07 (2011) 007 [arXiv:1105.2565] [INSPIRE].
C. Cheung, G.N. Remmen, C.-H. Shen and C. Wen, Pions as Gluons in Higher Dimensions, JHEP 04 (2018) 129 [arXiv:1709.04932] [INSPIRE].
C. Cheung and G.N. Remmen, Twofold Symmetries of the Pure Gravity Action, JHEP 01 (2017) 104 [arXiv:1612.03927] [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, B. Feng and T. Søndergaard, Gravity and Yang-Mills Amplitude Relations, Phys. Rev. D 82 (2010) 107702 [arXiv:1005.4367] [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
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2002.10470
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Cheung, C., Remmen, G.N. Entanglement and the double copy. J. High Energ. Phys. 2020, 100 (2020). https://doi.org/10.1007/JHEP05(2020)100
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2020)100