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From Twistor-Particle Models to Massive Amplitudes
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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In his twistor-particle programme of the 1970's, Roger Penrose introduced a representation of the massive particle phase space in terms of a pair of twistors subject to an internal symmetry group. Here we use this representation to introduce a chiral string whose target is a complexification of this space, extended so as to incorporate supersymmetry. We show that the gauge anomalies associated to the internal symmetry group vanish only for maximal supersymmetry, and that correlators in these string models describe amplitudes involving massive particles with manifest supersymmetry. The models and amplitude formulae exhibit a double copy structure from gauge theory on the Coulomb branch to gravity, although the graviton remains massless. The formulae are closely related to those obtained earlier by the authors expressed in terms of the polarised scattering equations.
Keywords: twistor theory, scattering amplitudes, ambitwistor string. 
@article{SIGMA_2022_18_a44,
     author = {Giulia Albonico and Yvonne Geyer and Lionel Mason},
     title = {From {Twistor-Particle} {Models} to {Massive} {Amplitudes}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2022},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a44/}
}
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Giulia Albonico; Yvonne Geyer; Lionel Mason. From Twistor-Particle Models to Massive Amplitudes. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a44/

[1] Albonico G., Geyer Y., Mason L., “Recursion and worldsheet formulae for 6d superamplitudes”, J. High Energy Phys., 2020:8 (2020), 066, 90 pp., arXiv: 2001.05928 | DOI | MR

[2] Albonico G., Geyer Y., Mason L., Massive ambitwistor string models, Parts I II, in preparation

[3] Arkani-Hamed N., Huang T.C., Huang Y., “Scattering amplitudes for all masses and spins”, J. High Energy Phys., 2021:11 (2021), 070, 75 pp., arXiv: 1709.04891 | DOI | MR

[4] Berkovits N., “Alternative string theory in twistor space for $N=4$ super-Yang–Mills theory”, Phys. Rev. Lett., 93 (2004), 011601, 3 pp., arXiv: hep-th/0402045 | DOI | MR

[5] Berkovits N., Lize M., “Field theory actions for ambitwistor string and superstring”, J. High Energy Phys., 2018:9 (2018), 097, 16 pp., arXiv: 1807.07661 | DOI | MR

[6] Bern Z., Carrasco J.J.M., Johansson H., “New relations for gauge-theory amplitudes”, Phys. Rev. D, 78 (2008), 085011, 19 pp., arXiv: 0805.3993 | DOI | MR

[7] Bern Z., Carrasco J.J.M., Johansson H., “Perturbative quantum gravity as a double copy of gauge theory”, Phys. Rev. Lett., 105 (2010), 061602, 4 pp., arXiv: 1004.0476 | DOI | MR

[8] Bette A., de Azcárraga J.A., Lukierski J., Miquel-Espanya C., “Massive relativistic free fields with Lorentz spins and electric charges”, Phys. Lett. B, 595 (2004), 491–497, arXiv: hep-th/0405166 | DOI | MR

[9] Bette A., Lukierski J., Miquel-Espanya C., “Two-twistor space, commuting composite Minkowski coordinates and particle dynamics”, Fundamental Interactions and Twistor-Like Methods, AIP Conf. Proc., 767, Amer. Inst. Phys., Melville, NY, 2005, 44–56, arXiv: hep-th/0503134 | DOI | MR

[10] Bjerrum-Bohr N.E.J., Bourjaily J.L., Damgaard P.H., Feng B., “Manifesting color-kinematics duality in the scattering equation formalism”, J. High Energy Phys., 2016:9 (2016), 094, 17 pp., arXiv: 1608.00006 | DOI | MR

[11] Cachazo F., Guevara A., Heydeman M., Mizera S., Schwarz J.H., Wen C., “The S matrix of 6D super Yang–Mills and maximal supergravity from rational maps”, J. High Energy Phys., 2018:9 (2018), 125, 85 pp., arXiv: 1805.11111 | DOI | MR

[12] Cachazo F., He S., Yuan E.Y., “Scattering in three dimensions from rational maps”, J. High Energy Phys., 2013:10 (2013), 141, 20 pp., arXiv: 1306.2962 | DOI | MR

[13] Cachazo F., He S., Yuan E.Y., “Scattering of massless particles in arbitrary dimensions”, Phys. Rev. Lett., 113 (2014), 171601, 4 pp., arXiv: 1307.2199 | DOI

[14] Cachazo F., He S., Yuan E.Y., “Scattering of massless particles: scalars, gluons and gravitons”, J. High Energy Phys., 2014:7 (2014), 033, 20 pp., arXiv: 1309.0885 | DOI

[15] Cachazo F., He S., Yuan E.Y., “Scattering equations and matrices: from Einstein to Yang–Mills, DBI and NLSM”, J. High Energy Phys., 2015:7 (2015), 149, 43 pp., arXiv: 1412.3479 | DOI | MR

[16] Cachazo F., Mason L., Skinner D., “Gravity in twistor space and its Grassmannian formulation”, SIGMA, 10 (2014), 051, 28 pp., arXiv: 1207.4712 | DOI | MR

[17] Cachazo F., Skinner D., “Gravity from rational curves in twistor space”, Phys. Rev. Lett., 110 (2013), 161301, 4 pp., arXiv: 1207.0741 | DOI

[18] Casali E., Geyer Y., Mason L., Monteiro R., Roehrig K.A., “New ambitwistor string theories”, J. High Energy Phys., 2015:11 (2015), 038, 29 pp., arXiv: 1506.08771 | DOI | MR

[19] Conde E., Joung E., Mkrtchyan K., “Spinor-helicity three-point amplitudes from local cubic interactions”, J. High Energy Phys., 2016:8 (2016), 040, 29 pp., arXiv: 1605.07402 | DOI | MR

[20] Conde E., Marzolla A., “Lorentz constraints on massive three-point amplitudes”, J. High Energy Phys., 2016:9 (2016), 041, 42 pp., arXiv: 1601.08113 | DOI | MR

[21] Craig N., Elvang H., Kiermaier M., Slatyer T.R., “Massive amplitudes on the Coulomb branch of $\mathcal N=4$ SYM”, J. High Energy Phys., 2011:12 (2011), 097, 38 pp., arXiv: 1104.2050 | DOI | MR

[22] de Azcarraga J.A., Fedoruk S., Izquierdo J.M., Lukierski J., “Two-twistor particle models and free massive higher spin fields”, J. High Energy Phys., 2015:4 (2015), 010, 39 pp., arXiv: 1409.7169 | DOI

[23] Deguchi S., Okano S., “Gauged twistor formulation of a massive spinning particle in four dimensions”, Phys. Rev. D, 93 (2016), 045016, 22 pp. | DOI | MR

[24] Deguchi S., Suzuki T., “Twistor formulation of a massive particle with rigidity”, Nuclear Phys. B, 932 (2018), 385–424, arXiv: 1707.04713 | DOI | MR

[25] Dolan L., Goddard P., “Proof of the formula of Cachazo, He and Yuan for Yang–Mills tree amplitudes in arbitrary dimension”, J. High Energy Phys., 2014:4 (2014), 010, 24 pp., arXiv: 1311.5200 | DOI | MR

[26] Fedoruk S., Lukierski J., “Massive twistor particle with spin generated by Souriau–Wess–Zumino term and its quantization”, Phys. Lett. B, 733 (2014), 309–315, arXiv: 1403.4127 | DOI

[27] Fedoruk S., Zima V.G., Bitwistor formulation of massive spinning particle, arXiv: hep-th/0308154

[28] Ferber A., “Supertwistors and conformal supersymmetry”, Nuclear Phys. B, 132 (1978), 55–64 | DOI | MR

[29] Geyer Y., Lipstein A.E., Mason L., “Ambitwistor strings in four dimensions”, Phys. Rev. Lett., 113 (2014), 081602, 5 pp., arXiv: 1404.6219 | DOI

[30] Geyer Y., Mason L., “Polarized scattering equations for 6D superamplitudes”, Phys. Rev. Lett., 122 (2019), 101601, 6 pp., arXiv: 1812.05548 | DOI

[31] Geyer Y., Mason L., “Supersymmetric S-matrices from the worldsheet in 10 11d”, Phys. Lett. B, 804 (2020), 135361, 6 pp., arXiv: 1901.00134 | DOI | MR

[32] Geyer Y., Mason L., Monteiro R., Tourkine P., “Loop integrands for scattering amplitudes from the Riemann sphere”, Phys. Rev. Lett., 115 (2015), 121603, 5 pp., arXiv: 1507.00321 | DOI | MR

[33] Geyer Y., Mason L., Monteiro R., Tourkine P., “One-loop amplitudes on the Riemann sphere”, J. High Energy Phys., 2016:3 (2016), 114, 53 pp., arXiv: 1511.06315 | DOI

[34] Geyer Y., Mason L., Skinner D., “Ambitwistor strings in six and five dimensions”, J. High Energy Phys., 2021:8 (2021), 153, 34 pp., arXiv: 2012.15172 | DOI | MR

[35] Herderschee A., Koren S., Trott T., “Constructing $\mathcal N=4$ Coulomb branch superamplitudes”, J. High Energy Phys., 2019:8 (2019), 107, 50 pp., arXiv: 1902.07205 | DOI | MR

[36] Hughston L.P., Twistors and particles, Lecture Notes in Physics, 97, Springer-Verlag, Berlin – New York, 1979 | DOI | MR

[37] Hughston L.P., Hurd T.R., “A cohomological description of massive fields”, Proc. Roy. Soc. London Ser. A, 378 (1981), 141–154 | DOI | MR

[38] Johansson H., Ochirov A., “Pure gravities via color-kinematics duality for fundamental matter”, J. High Energy Phys., 2015:11 (2015), 046, 52 pp., arXiv: 1407.4772 | DOI | MR

[39] Johansson H., Ochirov A., “Double copy for massive quantum particles with spin”, J. High Energy Phys., 2019:9 (2019), 040, 44 pp., arXiv: 1906.12292 | DOI | MR

[40] Kunz C., Four dimensional anomaly-free twistor string, arXiv: 2004.04842

[41] Kunz C., A note on classical aspects of the four dimensional anomaly-free twistor string, arXiv: 2104.06584

[42] Lazopoulos A., Ochirov A., Shi C., “All-multiplicity amplitudes with four massive quarks and identical-helicity gluons”, J. High Energy Phys., 2022:3 (2022), 009, 38 pp., arXiv: 2111.06847 | DOI

[43] Mason L.J., Reid-Edwards R.A., The supersymmetric Penrose transform in six dimensions, arXiv: 1212.6173

[44] Mason L.J., Reid-Edwards R.A., Taghavi-Chabert A., “Conformal field theories in six-dimensional twistor space”, J. Geom. Phys., 62 (2012), 2353–2375, arXiv: 1111.2585 | DOI | MR

[45] Mason L.J., Skinner D., “Ambitwistor strings and the scattering equations”, J. High Energy Phys., 2014:7 (2014), 048, 34 pp., arXiv: 1311.2564 | DOI | MR

[46] Monteiro R., O'Connell D., “The kinematic algebras from the scattering equations”, J. High Energy Phys., 2014:3 (2014), 110, 28 pp., arXiv: 1311.1151 | DOI | MR

[47] Naculich S.G., “Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles”, J. High Energy Phys., 2014:9 (2014), 029, 21 pp., arXiv: 1407.7836 | DOI

[48] Naculich S.G., “CHY representations for gauge theory and gravity amplitudes with up to three massive particles”, J. High Energy Phys., 2015:5 (2015), 050, 19 pp., arXiv: 1501.03500 | DOI | MR

[49] Ochirov A., “Helicity amplitudes for QCD with massive quarks”, J. High Energy Phys., 2018:4 (2018), 089, 22 pp., arXiv: 1802.06730 | DOI | MR

[50] Okano S., Deguchi S., “A no-go theorem for the $n$-twistor description of a massive particle”, J. Math. Phys., 58 (2017), 031701, 6 pp., arXiv: 1606.01339 | DOI | MR

[51] Penrose R., “Twistors and particles: an outline”, Quantum Theory and the Structure of Space-Time, Feldafing Conference of the Max-Planck Institute, Carl Hanser Verlag, Münich, 1975, 129–145

[52] Penrose R., “The twistor programme”, Rep. Math. Phys., 12 (1977), 65–76 | DOI | MR

[53] Penrose R., Rindler W., Spinors and space-time, v. 2, Cambridge Monographs on Mathematical Physics, Spinor and twistor methods in space-time geometry, Cambridge University Press, Cambridge, 1986 | DOI | MR

[54] Perjés Z., “Twistor variables of relativistic mechanics”, Phys. Rev. D, 11 (1975), 2031–2041 | DOI | MR

[55] Perjés Z., “Perspectives of Penrose theory in particle physics”, Rep. Math. Phys., 12 (1977), 193–211 | DOI | MR

[56] Reid-Edwards R., On closed twistor string theory, arXiv: 1212.6047

[57] Roehrig K.A., Skinner D., “A gluing operator for the ambitwistor string”, J. High Energy Phys., 2018:1 (2018), 069, 33 pp., arXiv: 1709.03262 | DOI | MR

[58] Roiban R., Spradlin M., Volovich A., “Tree-level $S$ matrix of Yang–Mills theory”, Phys. Rev. D, 70 (2004), 026009, 10 pp., arXiv: hep-th/0403190 | DOI | MR

[59] Roiban R., Volovich A., “All conjugate-maximal-helicity-violating amplitudes from topological open string theory in twistor space”, Phys. Rev. Lett., 93 (2004), 131602, 4 pp., arXiv: hep-th/0402121 | DOI | MR

[60] Sämann C., Wolf M., “On twistors and conformal field theories from six dimensions”, J. Math. Phys., 54 (2013), 013507, 44 pp., arXiv: 1111.2539 | DOI | MR

[61] Sämann C., Wolf M., “Non-abelian tensor multiplet equations from twistor space”, Comm. Math. Phys., 328 (2014), 527–544, arXiv: 1205.3108 | DOI | MR

[62] Schwarz J.H., Wen C., “Unified formalism for 6D superamplitudes based on a symplectic Grassmannian”, J. High Energy Phys., 2019:8 (2019), 125, 26 pp., arXiv: 1907.03485 | DOI | MR

[63] Skinner D., “Twistor strings for $\mathcal N=8$ supergravity”, J. High Energy Phys., 2020:4 (2020), 047, 50 pp., arXiv: 1301.0868 | DOI | MR

[64] Tod P., “Some symplectic forms arising in twistor theory”, Rep. Math. Phys., 11 (1977), 339–346 | DOI | MR

[65] Witten E., Superstring perturbation theory revisited, arXiv: 1209.5461

[66] Witten E., “Perturbative gauge theory as a string theory in twistor space”, Comm. Math. Phys., 252 (2004), 189–258, arXiv: hep-th/0312171 | DOI | MR