Abstract
We examine the double copy structure of anyons in gauge theory and gravity. Using on-shell amplitude techniques, we construct little group covariant spinor-helicity variables describing massive particles with spin, which together with locality and unitarity enables us to derive the long-range tree-level scattering amplitudes involving anyons. We discover that classical gauge theory anyon solutions double copy to their gravitational counterparts in a non-trivial manner. Interestingly, we show that the massless double copy captures the topological structure of curved spacetime in three dimensions by introducing a non-trivial mixing of the topological graviton and the dilaton. Finally, we show that the celebrated Aharonov-Bohm phase can be derived directly from the constructed on-shell amplitude, and that it too enjoys a simple double copy to its gravitational counterpart.
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References
F. Wilczek, Magnetic flux, angular momentum, and statistics, Phys. Rev. Lett. 48 (1982) 1144 [INSPIRE].
B.I. Halperin, Statistics of quasiparticles and the hierarchy of fractional quantized Hall states, Phys. Rev. Lett. 52 (1984) 1583 [Erratum ibid. 52 (1984) 2390] [INSPIRE].
R.B. Laughlin, The relationship between high temperature superconductivity and the fractional quantum Hall effect, Science 242 (1988) 525 [INSPIRE].
Y.M. Cho and D.H. Park, Causally spinning anyonic cosmic string, Phys. Rev. D 46 (1992) R1219 [INSPIRE].
W.T. Emond, Y.-T. Huang, U. Kol, N. Moynihan and D. O’Connell, Amplitudes from Coulomb to Kerr-Taub-NUT, arXiv:2010.07861 [INSPIRE].
N. Moynihan and J. Murugan, On-shell electric-magnetic duality and the dual graviton, arXiv:2002.11085 [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].
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].
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, J. Terning and M. Waterbury, Scattering amplitudes for monopoles: pairwise little group and pairwise helicity, JHEP 08 (2021) 029 [arXiv:2009.14213] [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].
G. Kälin, Z. Liu and R.A. Porto, Conservative dynamics of binary systems to third post-Minkowskian order from the effective field theory approach, Phys. Rev. Lett. 125 (2020) 261103 [arXiv:2007.04977] [INSPIRE].
G. Kälin, Z. Liu and R.A. Porto, Conservative tidal effects in compact binary systems to next-to-leading post-Minkowskian order, Phys. Rev. D 102 (2020) 124025 [arXiv:2008.06047] [INSPIRE].
G. Kälin and R.A. Porto, Post-Minkowskian effective field theory for conservative binary dynamics, JHEP 11 (2020) 106 [arXiv:2006.01184] [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].
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].
Z. Bern et al., Scattering Amplitudes and Conservative Binary Dynamics at \( \mathcal{O} \)(G4), Phys. Rev. Lett. 126 (2021) 171601 [arXiv:2101.07254] [INSPIRE].
Z. Bern, J. Parra-Martinez, R. Roiban, E. Sawyer and C.-H. Shen, Leading nonlinear tidal effects and scattering amplitudes, JHEP 05 (2021) 188 [arXiv:2010.08559] [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].
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].
L.A. Johnson, C.R.T. Jones and S. Paranjape, Constraints on a massive double-copy and applications to massive gravity, JHEP 02 (2021) 148 [arXiv:2004.12948] [INSPIRE].
A. Momeni, J. Rumbutis and A.J. Tolley, Massive gravity from double copy, JHEP 12 (2020) 030 [arXiv:2004.07853] [INSPIRE].
A. Momeni, J. Rumbutis and A.J. Tolley, Kaluza-Klein from colour-kinematics duality for massive fields, arXiv:2012.09711 [INSPIRE].
N. Moynihan, Scattering amplitudes and the double copy in topologically massive theories, JHEP 12 (2020) 163 [arXiv:2006.15957] [INSPIRE].
M. Carrillo González, B. Melcher, K. Ratliff, S. Watson and C.D. White, The classical double copy in three spacetime dimensions, JHEP 07 (2019) 167 [arXiv:1904.11001] [INSPIRE].
S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [INSPIRE].
A. Lerda, Anyons: quantum mechanics of particles with fractional statistics, Springer, Germany (2008).
D. Sen, An introduction to anyons, (1993).
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].
S. Deser and J.G. McCarthy, Spin and statistics of gravitational anyons, Nucl. Phys. B 344 (1990) 747 [INSPIRE].
P. de Sousa Gerbert and R. Jackiw, Classical and quantum scattering on a spinning cone, Commun. Math. Phys. 124 (1989) 229 [INSPIRE].
G. Clement, Stationary solutions with point sources in topologically massive gravity, Class. Quant. Grav. 7 (1990) L193 [INSPIRE].
B. Maybee, D. O’Connell and J. Vines, Observables and amplitudes for spinning particles and black holes, JHEP 12 (2019) 156 [arXiv:1906.09260] [INSPIRE].
A. Guevara, B. Maybee, A. Ochirov, D. O’connell and J. Vines, A worldsheet for Kerr, JHEP 03 (2021) 201 [arXiv:2012.11570] [INSPIRE].
S. Deser, R. Jackiw and G. ’t Hooft, Three-dimensional Einstein gravity: dynamics of flat space, Annals Phys. 152 (1984) 220 [INSPIRE].
N. Marcus and J.H. Schwarz, Three-dimensional supergravity theories, Nucl. Phys. B 228 (1983) 145 [INSPIRE].
A. Guevara, Holomorphic classical limit for spin effects in gravitational and electromagnetic scattering, JHEP 04 (2019) 033 [arXiv:1706.02314] [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].
V. Bargmann, Irreducible unitary representations of the Lorentz group, Annals Math. 48 (1947) 568 [INSPIRE].
Y.F. Bautista and A. Guevara, From scattering amplitudes to classical physics: universality, double copy and soft theorems, arXiv:1903.12419 [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].
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].
Y. Verbin, Lower dimensional gravity, Phys. Rev. D 50 (1994) 7318 [INSPIRE].
R. Jackiw, Topics in planar physics, Nucl. Phys. B Proc. Suppl. 18 (1990) 107.
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Gravitons in flatland, Springer Proc. Phys. 137 (2011) 291 [arXiv:1007.4561] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive gravity in three dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, More on massive 3D gravity, Phys. Rev. D 79 (2009) 124042 [arXiv:0905.1259] [INSPIRE].
A. Akhavan, M. Alishahiha, A. Naseh, A. Nemati and A. Shirzad, New bi-gravity from new massive gravity, JHEP 05 (2016) 006 [arXiv:1603.03270] [INSPIRE].
Z. Hlousek and D. Spector, Supersymmetric anyons, Nucl. Phys. B 344 (1990) 763 [INSPIRE].
C.D. White, Twistorial foundation for the classical double copy, Phys. Rev. Lett. 126 (2021) 061602 [arXiv:2012.02479] [INSPIRE].
E. Chacón, S. Nagy and C.D. White, The Weyl double copy from twistor space, JHEP 05 (2021) 2239 [arXiv:2103.16441] [INSPIRE].
K. Farnsworth, M.L. Graesser and G. Herczeg, Twistor space origins of the Newman-Penrose map, arXiv:2104.09525 [INSPIRE].
J. Ellis, TikZ-Feynman: Feynman diagrams with TikZ, Comput. Phys. Commun. 210 (2017) 103 [arXiv:1601.05437] [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.S. Plyushchay, The model of a free relativistic particle with fractional spin, Int. J. Mod. Phys. A 7 (1992) 7045 [INSPIRE].
R. Jackiw and V.P. Nair, Relativistic wave equations for anyons, Phys. Rev. D 43 (1991) 1933 [INSPIRE].
M.K. Gumus and G. Alkac, More on the classical double copy in three spacetime dimensions, Phys. Rev. D 102 (2020) 024074 [arXiv:2006.00552] [INSPIRE].
G. Alkac, M.K. Gumus and M.A. Olpak, Kerr-Schild double copy of the Coulomb solution in three dimensions, Phys. Rev. D 104 (2021) 044034 [arXiv:2105.11550] [INSPIRE].
S. Dengiz, E. Kilicarslan and B. Tekin, Scattering in topologically massive gravity, chiral gravity and the corresponding Anyon-Anyon potential energy, Phys. Rev. D 89 (2014) 024033 [arXiv:1311.4736] [INSPIRE].
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Burger, D.J., Emond, W.T. & Moynihan, N. Anyons and the double copy. J. High Energ. Phys. 2022, 17 (2022). https://doi.org/10.1007/JHEP01(2022)017
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DOI: https://doi.org/10.1007/JHEP01(2022)017