Abstract
We formulate Wilson loop observables as products of eikonal Wilson lines given in terms of on-shell scattering amplitudes. We derive the eikonal phases for dyons in both gauge theory and gravity, which we use to derive the Dirac-Schwinger-Zwanziger quantization condition and its relativistic gravitational (Taub-NUT) counterpart via the double copy. We also compute the Wilson loop for an anyon-anyon system, obtaining a relativistic generalisation of the Aharonov-Bohm phase for gravitational anyons.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. D. I. Abarbanel and C. Itzykson, Relativistic eikonal expansion, Phys. Rev. Lett. 23 (1969) 53 [INSPIRE].
S. J. Wallace and J. A. McNeil, Relativistic Eikonal Expansion, Phys. Rev. D 16 (1977) 3565 [INSPIRE].
H. Cheng and T. T. Wu, High-energy elastic scattering in quantum electrodynamics, Phys. Rev. Lett. 22 (1969) 666 [INSPIRE].
M. Levy and J. Sucher, Eikonal approximation in quantum field theory, Phys. Rev. 186 (1969) 1656 [INSPIRE].
D. N. Kabat and M. Ortiz, Eikonal quantum gravity and Planckian scattering, Nucl. Phys. B 388 (1992) 570 [hep-th/9203082] [INSPIRE].
R. Saotome and R. Akhoury, Relationship Between Gravity and Gauge Scattering in the High Energy Limit, JHEP 01 (2013) 123 [arXiv:1210.8111] [INSPIRE].
R. Akhoury, R. Saotome and G. Sterman, High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power, Phys. Rev. D 103 (2021) 064036 [arXiv:1308.5204] [INSPIRE].
M. Ciafaloni, D. Colferai, F. Coradeschi and G. Veneziano, Unified limiting form of graviton radiation at extreme energies, Phys. Rev. D 93 (2016) 044052 [arXiv:1512.00281] [INSPIRE].
N. E. J. Bjerrum-Bohr, J. F. Donoghue, B. R. Holstein, L. Plante and P. Vanhove, Light-like Scattering in Quantum Gravity, JHEP 11 (2016) 117 [arXiv:1609.07477] [INSPIRE].
A. Luna, S. Melville, S. G. Naculich and C. D. White, Next-to-soft corrections to high energy scattering in QCD and gravity, JHEP 01 (2017) 052 [arXiv:1611.02172] [INSPIRE].
N. E. J. Bjerrum-Bohr, P. H. Damgaard, G. Festuccia, L. Planté and P. Vanhove, General Relativity from Scattering Amplitudes, Phys. Rev. Lett. 121 (2018) 171601 [arXiv:1806.04920] [INSPIRE].
M. Ciafaloni, D. Colferai and G. Veneziano, Infrared features of gravitational scattering and radiation in the eikonal approach, Phys. Rev. D 99 (2019) 066008 [arXiv:1812.08137] [INSPIRE].
P. Di Vecchia, S. G. Naculich, R. Russo, G. Veneziano and C. D. White, A tale of two exponentiations in \( \mathcal{N} \) = 8 supergravity at subleading level, JHEP 03 (2020) 173 [arXiv:1911.11716] [INSPIRE].
P. Di Vecchia, A. Luna, S. G. Naculich, R. Russo, G. Veneziano and C. D. White, A tale of two exponentiations in \( \mathcal{N} \) = 8 supergravity, Phys. Lett. B 798 (2019) 134927 [arXiv:1908.05603] [INSPIRE].
A. Koemans Collado, P. Di Vecchia and R. Russo, Revisiting the second post-Minkowskian eikonal and the dynamics of binary black holes, Phys. Rev. D 100 (2019) 066028 [arXiv:1904.02667] [INSPIRE].
Z. Bern, H. Ita, J. Parra-Martinez and M.S. Ruf, Universality in the classical limit of massless gravitational scattering, Phys. Rev. Lett. 125 (2020) 031601 [arXiv:2002.02459] [INSPIRE].
J. Parra-Martinez, M. S. Ruf and M. Zeng, Extremal black hole scattering at (G3): graviton dominance, eikonal exponentiation, and differential equations, JHEP 11 (2020) 023 [arXiv:2005.04236] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, Universality of ultra-relativistic gravitational scattering, Phys. Lett. B 811 (2020) 135924 [arXiv:2008.12743] [INSPIRE].
G. Mogull, J. Plefka and J. Steinhoff, Classical black hole scattering from a worldline quantum field theory, JHEP 02 (2021) 048 [arXiv:2010.02865] [INSPIRE].
M. Accettulli Huber, A. Brandhuber, S. De Angelis and G. Travaglini, Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity, Phys. Rev. D 102 (2020) 046014 [arXiv:2006.02375] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, The eikonal approach to gravitational scattering and radiation at 𝒪(G3), JHEP 07 (2021) 169 [arXiv:2104.03256] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, Radiation Reaction from Soft Theorems, Phys. Lett. B 818 (2021) 136379 [arXiv:2101.05772] [INSPIRE].
G. U. Jakobsen, G. Mogull, J. Plefka and J. Steinhoff, Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory, Phys. Rev. Lett. 126 (2021) 201103 [arXiv:2101.12688] [INSPIRE].
C. Shi and J. Plefka, Classical double copy of worldline quantum field theory, Phys. Rev. D 105 (2022) 026007 [arXiv:2109.10345] [INSPIRE].
C. Heissenberg, Infrared divergences and the eikonal exponentiation, Phys. Rev. D 104 (2021) 046016 [arXiv:2105.04594] [INSPIRE].
K. Haddad, Exponentiation of the leading eikonal phase with spin, Phys. Rev. D 105 (2022) 026004 [arXiv:2109.04427] [INSPIRE].
E. Herrmann, J. Parra-Martinez, M. S. Ruf and M. Zeng, Radiative classical gravitational observables at (G3 ) from scattering amplitudes, JHEP 10 (2021) 148 [arXiv:2104.03957] [INSPIRE].
N. E. J. Bjerrum-Bohr, P. H. Damgaard, L. Planté and P. Vanhove, The amplitude for classical gravitational scattering at third Post-Minkowskian order, JHEP 08 (2021) 172 [arXiv:2105.05218] [INSPIRE].
M. Carrillo-González, C. de Rham and A. J. Tolley, Scattering amplitudes for binary systems beyond GR, JHEP 11 (2021) 087 [arXiv:2107.11384] [INSPIRE].
G. U. Jakobsen, G. Mogull, J. Plefka and J. Steinhoff, Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies, Phys. Rev. Lett. 128 (2022) 011101 [arXiv:2106.10256] [INSPIRE].
P. H. Damgaard, L. Plante and P. Vanhove, On an exponential representation of the gravitational S-matrix, JHEP 11 (2021) 213 [arXiv:2107.12891] [INSPIRE].
A. Brandhuber, G. Chen, G. Travaglini and C. Wen, Classical gravitational scattering from a gauge-invariant double copy, JHEP 10 (2021) 118 [arXiv:2108.04216] [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Superstring Collisions at Planckian Energies, Phys. Lett. B 197 (1987) 81 [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Higher Order Gravitational Deflection and Soft Bremsstrahlung in Planckian Energy Superstring Collisions, Nucl. Phys. B 347 (1990) 550 [INSPIRE].
M. Ciafaloni and D. Colferai, Rescattering corrections and self-consistent metric in Planckian scattering, JHEP 10 (2014) 085 [arXiv:1406.6540] [INSPIRE].
L. P. Gamberg and K. A. Milton, Dual quantum electrodynamics: Dyon-dyon and charge monopole scattering in a high-energy approximation, Phys. Rev. D 61 (2000) 075013 [hep-ph/9910526] [INSPIRE].
S. Caron-Huot, When does the gluon reggeize?, JHEP 05 (2015) 093 [arXiv:1309.6521] [INSPIRE].
K. Colwell and J. Terning, S-duality and Helicity Amplitudes, JHEP 03 (2016) 068 [arXiv:1510.07627] [INSPIRE].
Y.-T. Huang, U. Kol and D. O’Connell, Double copy of electric-magnetic duality, Phys. Rev. D 102 (2020) 046005 [arXiv:1911.06318] [INSPIRE].
R. Alawadhi, D. S. Berman, B. Spence and D. Peinador Veiga, S-duality and the double copy, JHEP 03 (2020) 059 [arXiv:1911.06797] [INSPIRE].
A. Banerjee, E. O. Colgáin, J. A. Rosabal and H. Yavartanoo, Ehlers as EM duality in the double copy, Phys. Rev. D 102 (2020) 126017 [arXiv:1912.02597] [INSPIRE].
N. Moynihan and J. Murugan, On-shell electric-magnetic duality and the dual graviton, Phys. Rev. D 105 (2022) 066025 [arXiv:2002.11085] [INSPIRE].
N. Moynihan, Scattering Amplitudes and the Double Copy in Topologically Massive Theories, JHEP 12 (2020) 163 [arXiv:2006.15957] [INSPIRE].
W. T. Emond, Y.-T. Huang, U. Kol, N. Moynihan and D. O’Connell, Amplitudes from Coulomb to Kerr-Taub-NUT, JHEP 05 (2022) 055 [arXiv:2010.07861] [INSPIRE].
C. Csáki, S. Hong, Y. Shirman, O. Telem, J. Terning and M. Waterbury, Scattering amplitudes for monopoles: pairwise little group and pairwise helicity, JHEP 08 (2021) 029 [arXiv:2009.14213] [INSPIRE].
J. Terning and C. B. Verhaaren, Spurious Poles in the Scattering of Electric and Magnetic Charges, JHEP 12 (2020) 153 [arXiv:2010.02232] [INSPIRE].
C. Csáki, S. Hong, Y. Shirman, O. Telem and J. Terning, Completing Multiparticle Representations of the Poincaré Group, Phys. Rev. Lett. 127 (2021) 041601 [arXiv:2010.13794] [INSPIRE].
A. Luna, R. Monteiro, D. O’Connell and C. D. White, The classical double copy for Taub-NUT spacetime, Phys. Lett. B 750 (2015) 272 [arXiv:1507.01869] [INSPIRE].
L. Alfonsi, C. D. White and S. Wikeley, Topology and Wilson lines: global aspects of the double copy, JHEP 07 (2020) 091 [arXiv:2004.07181] [INSPIRE].
N. Bahjat-Abbas, R. Stark-Muchão and C. D. White, Monopoles, shockwaves and the classical double copy, JHEP 04 (2020) 102 [arXiv:2001.09918] [INSPIRE].
J.-W. Kim and M. Shim, Gravitational Dyonic Amplitude at One-Loop and its Inconsistency with the Classical Impulse, JHEP 02 (2021) 217 [arXiv:2010.14347] [INSPIRE].
D. J. Burger, W. T. Emond and N. Moynihan, Anyons and the double copy, JHEP 01 (2022) 017 [arXiv:2103.10416] [INSPIRE].
N. Arkani-Hamed, Y.-t. Huang and D. O’Connell, Kerr black holes as elementary particles, JHEP 01 (2020) 046 [arXiv:1906.10100] [INSPIRE].
N. Moynihan, Kerr-Newman from Minimal Coupling, JHEP 01 (2020) 014 [arXiv:1909.05217] [INSPIRE].
W. T. Emond and N. Moynihan, Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity, JHEP 12 (2019) 019 [arXiv:1905.08213] [INSPIRE].
M.-Z. Chung, Y.-T. Huang, J.-W. Kim and S. Lee, The simplest massive S-matrix: from minimal coupling to Black Holes, JHEP 04 (2019) 156 [arXiv:1812.08752] [INSPIRE].
A. Guevara, A. Ochirov and J. Vines, Scattering of Spinning Black Holes from Exponentiated Soft Factors, JHEP 09 (2019) 056 [arXiv:1812.06895] [INSPIRE].
A. Guevara, A. Ochirov and J. Vines, Black-hole scattering with general spin directions from minimal-coupling amplitudes, Phys. Rev. D 100 (2019) 104024 [arXiv:1906.10071] [INSPIRE].
D. J. Burger, W. T. Emond and N. Moynihan, Rotating Black Holes in Cubic Gravity, Phys. Rev. D 101 (2020) 084009 [arXiv:1910.11618] [INSPIRE].
C. D. White, Factorization Properties of Soft Graviton Amplitudes, JHEP 05 (2011) 060 [arXiv:1103.2981] [INSPIRE].
R. Alawadhi, D. S. Berman, C. D. White and S. Wikeley, The single copy of the gravitational holonomy, JHEP 10 (2021) 229 [arXiv:2107.01114] [INSPIRE].
P. A. M. Dirac, Quantised singularities in the electromagnetic field, Proc. Roy. Soc. Lond. A 133 (1931) 60.
J. S. Schwinger, Magnetic charge and quantum field theory, Phys. Rev. 144 (1966) 1087 [INSPIRE].
D. Zwanziger, Exactly soluble nonrelativistic model of particles with both electric and magnetic charges, Phys. Rev. 176 (1968) 1480 [INSPIRE].
D. Zwanziger, Quantum field theory of particles with both electric and magnetic charges, Phys. Rev. 176 (1968) 1489 [INSPIRE].
J. S. Dowker and J. A. Roche, The Gravitational analogues of magnetic monopoles, Proc. Phys. Soc. 92 (1967) 1 [INSPIRE].
C. W. Misner, The Flatter regions of Newman, Unti and Tamburino’s generalized Schwarzschild space, J. Math. Phys. 4 (1963) 924 [INSPIRE].
J. S. Dowker, The nut solution as a gravitational dyon, Gen. Rel. Grav. 5 (1974) 603.
C. W. Bunster, S. Cnockaert, M. Henneaux and R. Portugues, Monopoles for gravitation and for higher spin fields, Phys. Rev. D 73 (2006) 105014 [hep-th/0601222] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-t. Huang, Scattering amplitudes for all masses and spins, JHEP 11 (2021) 070 [arXiv:1709.04891] [INSPIRE].
M. Blagojevic, S. Meljanac and P. Senjanovic, Radiation damping as a mechanism for partial confinement of magnetic monopoles, Phys. Lett. B 131 (1983) 111 [INSPIRE].
M. Blagojevic and P. Senjanovic, The Quantum Field Theory of Electric and Magnetic Charge, Phys. Rept. 157 (1988) 233 [INSPIRE].
D. R. Green, Worldlines as Wilson Lines, Phys. Rev. D 78 (2008) 064066 [arXiv:0804.4450] [INSPIRE].
A. Brandhuber, P. Heslop, A. Nasti, B. Spence and G. Travaglini, Four-point Amplitudes in N = 8 Supergravity and Wilson Loops, Nucl. Phys. B 807 (2009) 290 [arXiv:0805.2763] [INSPIRE].
R. Argurio, F. Dehouck and L. Houart, Supersymmetry and Gravitational Duality, Phys. Rev. D 79 (2009) 125001 [arXiv:0810.4999] [INSPIRE].
R. Jackiw, Topics in Planar Physics, Nucl. Phys. (Proc. Suppl.) 18 (1990) 107.
S. Deser and J. G. McCarthy, Spin and Statistics of Gravitational Anyons, Nucl. Phys. B 344 (1990) 747 [INSPIRE].
S. Deser, Gravitational anyons, Phys. Rev. Lett. 64 (1990) 611 [INSPIRE].
M. E. Ortiz, Gravitational anyons, Chern-Simons-Witten gravity and the gravitational Aharonov-Bohm effect, Nucl. Phys. B 363 (1991) 185 [INSPIRE].
R. Argurio, F. Dehouck and L. Houart, Boosting Taub-NUT to a BPS NUT-wave, JHEP 01 (2009) 045 [arXiv:0811.0538] [INSPIRE].
D. Bonocore, Asymptotic dynamics on the worldline for spinning particles, JHEP 02 (2021) 007 [arXiv:2009.07863] [INSPIRE].
L. de la Cruz, B. Maybee, D. O’Connell and A. Ross, Classical Yang-Mills observables from amplitudes, JHEP 12 (2020) 076 [arXiv:2009.03842] [INSPIRE].
L. de la Cruz, A. Luna and T. Scheopner, Yang-Mills observables: from KMOC to eikonal through EFT, JHEP 01 (2022) 045 [arXiv:2108.02178] [INSPIRE].
D. Bonocore, A. Kulesza and J. Pirsch, Classical and quantum gravitational scattering with Generalized Wilson Lines, JHEP 03 (2022) 147 [arXiv:2112.02009] [INSPIRE].
A. Cristofoli, Gravitational shock waves and scattering amplitudes, JHEP 11 (2020) 160 [arXiv:2006.08283] [INSPIRE].
G. Kälin and R. A. Porto, From Boundary Data to Bound States, JHEP 01 (2020) 072 [arXiv:1910.03008] [INSPIRE].
G. Kälin and R. A. Porto, From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist), JHEP 02 (2020) 120 [arXiv:1911.09130] [INSPIRE].
R. Gonzo and C. Shi, Geodesics from classical double copy, Phys. Rev. D 104 (2021) 105012 [arXiv:2109.01072] [INSPIRE].
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: 2109.11531
Rights and permissions
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.
About this article
Cite this article
Emond, W.T., Moynihan, N. & Wei, L. Quantization conditions and the double copy. J. High Energ. Phys. 2022, 108 (2022). https://doi.org/10.1007/JHEP09(2022)108
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2022)108