Yang-Mills form factors on self-dual backgrounds. (English) Zbl 07749040
Summary: The construction of perturbative quantities on non-linear backgrounds leads to the possibility of incorporating strong field effects in perturbation theory. We continue a programme to construct QFT observables on self-dual backgrounds in Yang-Mills theory. The approach works with asymptotic data for fields defined at null infinity \(\mathscr{I}\), extending earlier work on Yang-Mills amplitudes on self-dual backgrounds to form factors and further incorporating supersymmetry. Since our analysis is based on reconstruction from data at null infinity, it naturally ties into work on celestial and twisted holography. We study form factors both in pure Yang-Mills and their supersymmetric counterparts in \(\mathcal{N} = 4\) SYM, giving a full treatment of \(\mathcal{N} = 4\) super-Yang-Mills at null infinity and their self-dual nonlinear backgrounds. We obtain tree-level MHV form factors around these backgrounds using new formulae for lifting operators to twistor space leading to simple dressings of the corresponding form factors around the vacuum. We give brief indications on how to go beyond the MHV sector by introducing dressed versions of the MHV diagram propagator. We discuss generating functionals of the MHV all plus 1-loop amplitude in this context together with its various dual conformal representations.
MSC:
| 81-XX | Quantum theory |
References:
| [1] | R. Penrose, Nonlinear gravitons and curved twistor theory, Gen. Rel. Grav.7 (1976) 31 [INSPIRE]. · Zbl 0354.53025 |
| [2] | R.S. Ward, On selfdual gauge fields, Phys. Lett. A61 (1977) 81 [INSPIRE]. · Zbl 0964.81519 |
| [3] | L.J. Mason and N.M.J. Woodhouse, Integrability, selfduality, and twistor theory, Oxford University Press (1991) [INSPIRE]. |
| [4] | R.S. Ward and R.O. Wells, Twistor geometry and field theory, Cambridge University Press (1991) [doi:10.1017/CBO9780511524493] [INSPIRE]. · Zbl 0729.53068 |
| [5] | S.J. Parke and T.R. Taylor, An amplitude for n gluon scattering, Phys. Rev. Lett.56 (1986) 2459 [INSPIRE]. |
| [6] | V.P. Nair, A current algebra for some gauge theory amplitudes, Phys. Lett. B214 (1988) 215 [INSPIRE]. |
| [7] | Witten, E., Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys., 252, 189 (2004) · Zbl 1105.81061 · doi:10.1007/s00220-004-1187-3 |
| [8] | Berkovits, N., An alternative string theory in twistor space for N = 4 super-Yang-Mills, Phys. Rev. Lett., 93 (2004) · doi:10.1103/PhysRevLett.93.011601 |
| [9] | Roiban, R.; Spradlin, M.; Volovich, A., On the tree level S matrix of Yang-Mills theory, Phys. Rev. D, 70 (2004) · doi:10.1103/PhysRevD.70.026009 |
| [10] | Cachazo, F.; Svrcek, P.; Witten, E., MHV vertices and tree amplitudes in gauge theory, JHEP, 09, 006 (2004) · doi:10.1088/1126-6708/2004/09/006 |
| [11] | Britto, R.; Cachazo, F.; Feng, B.; Witten, E., Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett., 94 (2005) · doi:10.1103/PhysRevLett.94.181602 |
| [12] | Brandhuber, A.; Heslop, P.; Travaglini, G., A note on dual superconformal symmetry of the N = 4 super Yang-Mills S-matrix, Phys. Rev. D, 78 (2008) · doi:10.1103/PhysRevD.78.125005 |
| [13] | Bern, Z.; Carrasco, JJM; Johansson, H., Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett., 105 (2010) · doi:10.1103/PhysRevLett.105.061602 |
| [14] | Arkani-Hamed, N., The all-loop integrand for scattering amplitudes in planar N = 4 SYM, JHEP, 01, 041 (2011) · Zbl 1214.81141 · doi:10.1007/JHEP01(2011)041 |
| [15] | Cachazo, F.; He, S.; Yuan, EY, Scattering of massless particles in arbitrary dimensions, Phys. Rev. Lett., 113 (2014) · doi:10.1103/PhysRevLett.113.171601 |
| [16] | F. Cachazo, S. He and E.Y. Yuan, Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM, JHEP07 (2015) 149 [arXiv:1412.3479] [INSPIRE]. · Zbl 1388.83196 |
| [17] | Geyer, Y.; Lipstein, AE; Mason, LJ, Ambitwistor strings in four dimensions, Phys. Rev. Lett., 113 (2014) · doi:10.1103/PhysRevLett.113.081602 |
| [18] | L.J. Dixon, Calculating scattering amplitudes efficiently, in the proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 95): QCD and beyond, (1996), p. 539 [hep-ph/9601359] [INSPIRE]. |
| [19] | Bern, Z.; Dixon, LJ; Kosower, DA, On-shell methods in perturbative QCD, Annals Phys., 322, 1587 (2007) · Zbl 1122.81077 · doi:10.1016/j.aop.2007.04.014 |
| [20] | H. Elvang and Y.-T. Huang, Scattering amplitudes, arXiv:1308.1697 [INSPIRE]. |
| [21] | Travaglini, G., The SAGEX review on scattering amplitudes, J. Phys. A, 55 (2022) · doi:10.1088/1751-8121/ac8380 |
| [22] | Y. Geyer and L. Mason, The SAGEX review on scattering amplitudes. Chapter 6: ambitwistor strings and amplitudes from the worldsheet, J. Phys. A55 (2022) 443007 [arXiv:2203.13017] [INSPIRE]. · Zbl 1520.81101 |
| [23] | Chalmers, G.; Siegel, W., The selfdual sector of QCD amplitudes, Phys. Rev. D, 54, 7628 (1996) · doi:10.1103/PhysRevD.54.7628 |
| [24] | Mason, LJ, Twistor actions for non-self-dual fields: a derivation of twistor-string theory, JHEP, 10, 009 (2005) · doi:10.1088/1126-6708/2005/10/009 |
| [25] | Boels, R.; Mason, LJ; Skinner, D., Supersymmetric gauge theories in twistor space, JHEP, 02, 014 (2007) · doi:10.1088/1126-6708/2007/02/014 |
| [26] | Boels, R.; Mason, LJ; Skinner, D., From twistor actions to MHV diagrams, Phys. Lett. B, 648, 90 (2007) · Zbl 1248.81133 · doi:10.1016/j.physletb.2007.02.058 |
| [27] | Mason, LJ; Skinner, D., The complete planar S-matrix of N = 4 SYM as a Wilson loop in twistor space, JHEP, 12, 018 (2010) · Zbl 1294.81122 · doi:10.1007/JHEP12(2010)018 |
| [28] | Adamo, T.; Mason, L., MHV diagrams in twistor space and the twistor action, Phys. Rev. D, 86 (2012) · doi:10.1103/PhysRevD.86.065019 |
| [29] | Adamo, T.; Bullimore, M.; Mason, L.; Skinner, D., Scattering amplitudes and Wilson loops in twistor space, J. Phys. A, 44 (2011) · Zbl 1270.81129 · doi:10.1088/1751-8113/44/45/454008 |
| [30] | T. Adamo, Twistor actions for gauge theory and gravity, Ph.D. thesis, University of Oxford, Oxford, U.K. (2013) [arXiv:1308.2820] [INSPIRE]. |
| [31] | A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE]. · Zbl 1408.83003 |
| [32] | Costello, K.; Paquette, NM, Celestial holography meets twisted holography: 4d amplitudes from chiral correlators, JHEP, 10, 193 (2022) · Zbl 1534.83110 · doi:10.1007/JHEP10(2022)193 |
| [33] | Adamo, T.; Mason, L.; Sharma, A., Celestial amplitudes and conformal soft theorems, Class. Quant. Grav., 36 (2019) · Zbl 1478.81036 · doi:10.1088/1361-6382/ab42ce |
| [34] | A. Strominger, w_1+∞and the celestial sphere, arXiv:2105.14346 [INSPIRE]. |
| [35] | Ball, A.; Narayanan, SA; Salzer, J.; Strominger, A., Perturbatively exact w_1+∞asymptotic symmetry of quantum self-dual gravity, JHEP, 01, 114 (2022) · Zbl 1521.81284 · doi:10.1007/JHEP01(2022)114 |
| [36] | A. Strominger, w_1+∞algebra and the celestial sphere: infinite towers of soft graviton, photon, and gluon symmetries, Phys. Rev. Lett.127 (2021) 221601 [INSPIRE]. |
| [37] | E.T. Newman, Heaven and its properties, Gen. Rel. Grav.7 (1976) 107 [INSPIRE]. |
| [38] | R.O. Hansen, E.T. Newman, R. Penrose and K.P. Tod, The metric and curvature properties of H space, Proc. Roy. Soc. Lond. A363 (1978) 445 [INSPIRE]. · Zbl 0391.53014 |
| [39] | G.A.J. Sparling, Dynamically broken symmetry and global Yang-Mills in Minkowski space, in Further advances in twistor theory, volume 231, chapter 1.4.2, L.J. Mason and L.P. Hughston eds., Pitman Research Notes in Mathematics (1990). · Zbl 0693.53022 |
| [40] | E.T. Newman, Source-free Yang-Mills theories, Phys. Rev. D18 (1978) 2901 [INSPIRE]. |
| [41] | Adamo, T.; Mason, L.; Sharma, A., Celestial w_1+∞symmetries from twistor space, SIGMA, 18, 016 (2022) · Zbl 1489.83067 |
| [42] | Adamo, T.; Bu, W.; Casali, E.; Sharma, A., All-order celestial OPE in the MHV sector, JHEP, 03, 252 (2023) · doi:10.1007/JHEP03(2023)252 |
| [43] | Brandhuber, A.; Spence, B.; Travaglini, G.; Yang, G., Form factors in N = 4 super Yang-Mills and periodic Wilson loops, JHEP, 01, 134 (2011) · Zbl 1214.81146 · doi:10.1007/JHEP01(2011)134 |
| [44] | Brandhuber, A., Harmony of super form factors, JHEP, 10, 046 (2011) · Zbl 1303.81111 · doi:10.1007/JHEP10(2011)046 |
| [45] | Brandhuber, A.; Travaglini, G.; Yang, G., Analytic two-loop form factors in N = 4 SYM, JHEP, 05, 082 (2012) · Zbl 1348.81400 · doi:10.1007/JHEP05(2012)082 |
| [46] | Penante, B.; Spence, B.; Travaglini, G.; Wen, C., On super form factors of half-BPS operators in N = 4 super Yang-Mills, JHEP, 04, 083 (2014) · doi:10.1007/JHEP04(2014)083 |
| [47] | Brandhuber, A., The connected prescription for form factors in twistor space, JHEP, 11, 143 (2016) · Zbl 1390.81571 · doi:10.1007/JHEP11(2016)143 |
| [48] | He, S.; Liu, Z., A note on connected formula for form factors, JHEP, 12, 006 (2016) · Zbl 1390.81325 · doi:10.1007/JHEP12(2016)006 |
| [49] | Brandhuber, A.; Kostacinska, M.; Penante, B.; Travaglini, G., Higgs amplitudes from N = 4 super Yang-Mills theory, Phys. Rev. Lett., 119 (2017) · doi:10.1103/PhysRevLett.119.161601 |
| [50] | A. Brandhuber, M. Kostacinska, B. Penante and G. Travaglini, Tr(F^3) supersymmetric form factors and maximal transcendentality. Part II. \(0 < \mathcal{N} < 4\) super Yang-Mills, JHEP12 (2018) 077 [arXiv:1804.05828] [INSPIRE]. · Zbl 1405.81147 |
| [51] | A. Brandhuber, M. Kostacinska, B. Penante and G. Travaglini, Tr(F^3) supersymmetric form factors and maximal transcendentality. Part I. N = 4 super Yang-Mills, JHEP12 (2018) 076 [arXiv:1804.05703] [INSPIRE]. |
| [52] | Bianchi, L.; Brandhuber, A.; Panerai, R.; Travaglini, G., Form factor recursion relations at loop level, JHEP, 02, 182 (2019) · Zbl 1411.81202 · doi:10.1007/JHEP02(2019)182 |
| [53] | Bianchi, L.; Brandhuber, A.; Panerai, R.; Travaglini, G., Dual conformal invariance for form factors, JHEP, 02, 134 (2019) · Zbl 1411.81201 · doi:10.1007/JHEP02(2019)134 |
| [54] | M. Accettulli Huber, A. Brandhuber, S. De Angelis and G. Travaglini, Complete form factors in Yang-Mills from unitarity and spinor helicity in six dimensions, Phys. Rev. D101 (2020) 026004 [arXiv:1910.04772] [INSPIRE]. |
| [55] | Adamo, T.; Bullimore, M.; Mason, L.; Skinner, D., A proof of the supersymmetric correlation function/Wilson loop correspondence, JHEP, 08, 076 (2011) · Zbl 1298.81152 · doi:10.1007/JHEP08(2011)076 |
| [56] | Eden, B.; Heslop, P.; Mason, L., The correlahedron, JHEP, 09, 156 (2017) · Zbl 1382.81139 · doi:10.1007/JHEP09(2017)156 |
| [57] | Koster, L.; Mitev, V.; Staudacher, M.; Wilhelm, M., Composite operators in the twistor formulation of N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett., 117 (2016) · doi:10.1103/PhysRevLett.117.011601 |
| [58] | Koster, L.; Mitev, V.; Staudacher, M.; Wilhelm, M., All tree-level MHV form factors in N = 4 SYM from twistor space, JHEP, 06, 162 (2016) · Zbl 1388.81338 · doi:10.1007/JHEP06(2016)162 |
| [59] | Koster, L.; Mitev, V.; Staudacher, M.; Wilhelm, M., On form factors and correlation functions in twistor space, JHEP, 03, 131 (2017) · Zbl 1377.83054 · doi:10.1007/JHEP03(2017)131 |
| [60] | Chicherin, D.; Sokatchev, E., Demystifying the twistor construction of composite operators in N = 4 super-Yang-Mills theory, J. Phys. A, 50 (2017) · Zbl 1367.81108 · doi:10.1088/1751-8121/aa6b95 |
| [61] | Chicherin, D.; Heslop, P.; Korchemsky, GP; Sokatchev, E., Wilson loop form factors: a new duality, JHEP, 04, 029 (2018) · Zbl 1390.81577 · doi:10.1007/JHEP04(2018)029 |
| [62] | D. Chicherin and E. Sokatchev, N = 4 super-Yang-Mills in LHC superspace. Part I. Classical and quantum theory, JHEP02 (2017) 062 [arXiv:1601.06803] [INSPIRE]. |
| [63] | D. Chicherin and E. Sokatchev, N = 4 super-Yang-Mills in LHC superspace. Part II. Non-chiral correlation functions of the stress-tensor multiplet, JHEP03 (2017) 048 [arXiv:1601.06804] [INSPIRE]. |
| [64] | Chicherin, D., Correlation functions of the chiral stress-tensor multiplet in N = 4 SYM, JHEP, 06, 198 (2015) · Zbl 1388.81035 · doi:10.1007/JHEP06(2015)198 |
| [65] | Casali, E.; Melton, W.; Strominger, A., Celestial amplitudes as AdS-Witten diagrams, JHEP, 11, 140 (2022) · Zbl 1536.81179 · doi:10.1007/JHEP11(2022)140 |
| [66] | Melton, W.; Narayanan, SA; Strominger, A., Deforming soft algebras for gauge theory, JHEP, 03, 233 (2023) · Zbl 07690797 · doi:10.1007/JHEP03(2023)233 |
| [67] | W.H. Furry, On bound states and scattering in positron theory, Phys. Rev.81 (1951) 115 [INSPIRE]. · Zbl 0042.45402 |
| [68] | B.S. DeWitt, Quantum theory of gravity. 2. The manifestly covariant theory, Phys. Rev.162 (1967) 1195 [INSPIRE]. · Zbl 0161.46501 |
| [69] | G. ’t Hooft, The background field method in gauge field theories, in the proceedings of the 12^thannual winter school of theoretical physics, (1975) [INSPIRE]. |
| [70] | L.F. Abbott, Introduction to the background field method, Acta Phys. Polon. B13 (1982) 33 [INSPIRE]. |
| [71] | Adamo, T.; Casali, E.; Mason, L.; Nekovar, S., Scattering on plane waves and the double copy, Class. Quant. Grav., 35 (2018) · Zbl 1382.83035 · doi:10.1088/1361-6382/aa9961 |
| [72] | Adamo, T.; Casali, E.; Mason, L.; Nekovar, S., Amplitudes on plane waves from ambitwistor strings, JHEP, 11, 160 (2017) · Zbl 1383.83143 · doi:10.1007/JHEP11(2017)160 |
| [73] | Adamo, T.; Casali, E.; Mason, L.; Nekovar, S., Plane wave backgrounds and colour-kinematics duality, JHEP, 02, 198 (2019) · Zbl 1411.81216 · doi:10.1007/JHEP02(2019)198 |
| [74] | Adamo, T.; Ilderton, A., Classical and quantum double copy of back-reaction, JHEP, 09, 200 (2020) · Zbl 1454.83028 · doi:10.1007/JHEP09(2020)200 |
| [75] | Adamo, T.; Ilderton, A.; MacLeod, AJ, One-loop multicollinear limits from 2-point amplitudes on self-dual backgrounds, JHEP, 12, 207 (2021) · Zbl 1521.81366 · doi:10.1007/JHEP12(2021)207 |
| [76] | Adamo, T.; Mason, L.; Sharma, A., MHV scattering of gluons and gravitons in chiral strong fields, Phys. Rev. Lett., 125 (2020) · doi:10.1103/PhysRevLett.125.041602 |
| [77] | Adamo, T.; Mason, L.; Sharma, A., Gluon scattering on self-dual radiative gauge fields, Commun. Math. Phys., 399, 1731 (2023) · Zbl 1522.81675 · doi:10.1007/s00220-022-04582-9 |
| [78] | Adamo, T.; Mason, L.; Sharma, A., Graviton scattering in self-dual radiative space-times, Class. Quant. Grav., 40 (2023) · Zbl 1521.81188 · doi:10.1088/1361-6382/acc233 |
| [79] | G. Chalmers and W. Siegel, Dual formulations of Yang-Mills theory, hep-th/9712191 [INSPIRE]. |
| [80] | Costello, K.; Paquette, NM, Associativity of one-loop corrections to the celestial operator product expansion, Phys. Rev. Lett., 129 (2022) · doi:10.1103/PhysRevLett.129.231604 |
| [81] | Bu, W.; Casali, E., The 4d/2d correspondence in twistor space and holomorphic Wilson lines, JHEP, 11, 076 (2022) · Zbl 1536.81159 · doi:10.1007/JHEP11(2022)076 |
| [82] | Costello, K.; Paquette, NM; Sharma, A., Top-down holography in an asymptotically flat spacetime, Phys. Rev. Lett., 130 (2023) · doi:10.1103/PhysRevLett.130.061602 |
| [83] | D.M. Wolkow, Über eine Klasse von Lösungen der Diracschen Gleichung (in German), Z. Phys.94 (1935) 250 [INSPIRE]. · Zbl 0011.18502 |
| [84] | D. Seipt, Volkov states and non-linear Compton scattering in short and intense laser pulses, in the proceedings of the Quantum field theory at the limits: from strong fields to heavy quarks, (2017), p. 24 [doi:10.3204/DESY-PROC-2016-04/Seipt] [arXiv:1701.03692] [INSPIRE]. |
| [85] | Dixon, LJ; Glover, EWN; Khoze, VV, MHV rules for Higgs plus multi-gluon amplitudes, JHEP, 12, 015 (2004) · doi:10.1088/1126-6708/2004/12/015 |
| [86] | Henn, J.; Power, B.; Zoia, S., Conformal invariance of the one-loop all-plus helicity scattering amplitudes, JHEP, 02, 019 (2020) · Zbl 1435.81239 · doi:10.1007/JHEP02(2020)019 |
| [87] | Chicherin, D.; Henn, JM, Symmetry properties of Wilson loops with a Lagrangian insertion, JHEP, 07, 057 (2022) · Zbl 1522.81611 · doi:10.1007/JHEP07(2022)057 |
| [88] | R. Penrose and W. Rindler, Spinors and space-time, Cambridge University Press, Cambridge, U.K. (2011) [doi:10.1017/CBO9780511564048] [INSPIRE]. |
| [89] | T. Adamo, Lectures on twistor theory, PoSModave2017 (2018) 003 [arXiv:1712.02196] [INSPIRE]. |
| [90] | M.G.T. van der Burg, Gravitational waves in general relativity X. Asymptotic expansions for the Einstein-Maxwell field, Proc. Roy. Soc. Lond. A310 (1969) 221. |
| [91] | Strominger, A., Asymptotic symmetries of Yang-Mills theory, JHEP, 07, 151 (2014) · Zbl 1333.81273 · doi:10.1007/JHEP07(2014)151 |
| [92] | Barnich, G.; Lambert, P-H, Einstein-Yang-Mills theory: asymptotic symmetries, Phys. Rev. D, 88 (2013) · doi:10.1103/PhysRevD.88.103006 |
| [93] | R. Penrose, Asymptotic properties of fields and space-times, Phys. Rev. Lett.10 (1963) 66 [INSPIRE]. |
| [94] | R. Penrose, Null hypersurface initial data for classical fields of arbitrary spin and for general relativity, Gen. Rel. Grav.12 (1980) 225 [INSPIRE]. · Zbl 0452.53014 |
| [95] | R. Penrose and W. Rindler, Spinors and space-time, Cambridge University Press, Cambridge, U.K. (2011) [doi:10.1017/CBO9780511564048] [INSPIRE]. |
| [96] | R. Penrose, Twistor algebra, J. Math. Phys.8 (1967) 345 [INSPIRE]. · Zbl 0163.22602 |
| [97] | L.J. Mason, Dolbeault representative from characteristic initial data at null infinity, in Further advances in twistor theory, volume 231, chapter 1.2.16, L.J. Mason and L.P. Hughston eds., Pitman Research Notes in Mathematics (1990). · Zbl 0693.53022 |
| [98] | R. Penrose, Solutions of the zero-rest-mass equations, J. Math. Phys.10 (1969) 38 [INSPIRE]. |
| [99] | M.G. Eastwood, R. Penrose and R.O. Wells, Cohomology and massless fields, Commun. Math. Phys.78 (1981) 305 [INSPIRE]. · Zbl 0465.58031 |
| [100] | E.T. Newman, Selfdual gauge fields, Phys. Rev. D22 (1980) 3023 [INSPIRE]. |
| [101] | E. Witten, An interpretation of classical Yang-Mills theory, Phys. Lett. B77 (1978) 394 [INSPIRE]. |
| [102] | J.P. Harnad and S. Shnider, Constraints and field equations for ten-dimensional super-Yang-mills theory, Commun. Math. Phys.106 (1986) 183 [INSPIRE]. · Zbl 0601.53071 |
| [103] | E. Witten, Twistor-like transform in ten-dimensions, Nucl. Phys. B266 (1986) 245 [INSPIRE]. · Zbl 0608.53068 |
| [104] | Devchand, C.; Ogievetsky, V., Interacting fields of arbitrary spin and N > 4 supersymmetric selfdual Yang-Mills equations, Nucl. Phys. B, 481, 188 (1996) · Zbl 0925.81369 |
| [105] | A. Ferber, Supertwistors and conformal supersymmetry, Nucl. Phys. B132 (1978) 55 [INSPIRE]. |
| [106] | I.V. Volovich, Supersymmetric Yang-Mills theories and twistors, Phys. Lett. B129 (1983) 429 [INSPIRE]. |
| [107] | I.V. Volovich, Superselfduality for supersymmetric Yang-Mills theory, Phys. Lett. B123 (1983) 329 [INSPIRE]. |
| [108] | Adamo, T.; Cristofoli, A.; Tourkine, P., Eikonal amplitudes from curved backgrounds, SciPost Phys., 13, 032 (2022) · doi:10.21468/SciPostPhys.13.2.032 |
| [109] | Mason, LJ; Skinner, D., Gravity, twistors and the MHV formalism, Commun. Math. Phys., 294, 827 (2010) · Zbl 1226.81146 · doi:10.1007/s00220-009-0972-4 |
| [110] | Boels, RH; Isermann, RS; Monteiro, R.; O’Connell, D., Colour-kinematics duality for one-loop rational amplitudes, JHEP, 04, 107 (2013) · doi:10.1007/JHEP04(2013)107 |
| [111] | Rosly, AA; Selivanov, KG, On amplitudes in selfdual sector of Yang-Mills theory, Phys. Lett. B, 399, 135 (1997) · doi:10.1016/S0370-2693(97)00268-2 |
| [112] | Selivanov, KG, On tree form-factors in (supersymmetric) Yang-Mills theory, Commun. Math. Phys., 208, 671 (2000) · Zbl 1052.81070 · doi:10.1007/s002200050006 |
| [113] | Mason, LJ; Skinner, D., Gravity, twistors and the MHV formalism, Commun. Math. Phys., 294, 827 (2010) · Zbl 1226.81146 · doi:10.1007/s00220-009-0972-4 |
| [114] | Adamo, T.; Ilderton, A., Gluon helicity flip in a plane wave background, JHEP, 06, 015 (2019) · doi:10.1007/JHEP06(2019)015 |
| [115] | M.F. Atiyah, Green’s functions for selfdual four manifolds, Adv. Math. Suppl. Stud.7 (1981) 129 [INSPIRE]. · Zbl 0484.53036 |
| [116] | Lipstein, AE; Mason, L., From the holomorphic Wilson loop to ‘d log’ loop-integrands for super-Yang-Mills amplitudes, JHEP, 05, 106 (2013) · Zbl 1342.81216 · doi:10.1007/JHEP05(2013)106 |
| [117] | Lipstein, AE; Mason, L., From d logs to dilogs the super Yang-Mills MHV amplitude revisited, JHEP, 01, 169 (2014) · doi:10.1007/JHEP01(2014)169 |
| [118] | Z. Bern, G. Chalmers, L.J. Dixon and D.A. Kosower, One loop N gluon amplitudes with maximal helicity violation via collinear limits, Phys. Rev. Lett.72 (1994) 2134 [hep-ph/9312333] [INSPIRE]. |
| [119] | G. Mahlon, Multi-gluon helicity amplitudes involving a quark loop, Phys. Rev. D49 (1994) 4438 [hep-ph/9312276] [INSPIRE]. |
| [120] | Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop gauge theory amplitudes with an arbitrary number of external legs, in the proceedings of the Workshop on continuous advances in QCD, (1994) [hep-ph/9405248] [INSPIRE]. |
| [121] | Boels, R., A quantization of twistor Yang-Mills theory through the background field method, Phys. Rev. D, 76 (2007) · doi:10.1103/PhysRevD.76.105027 |
| [122] | Bullimore, M.; Mason, LJ; Skinner, D., MHV diagrams in momentum twistor space, JHEP, 12, 032 (2010) · Zbl 1294.81094 · doi:10.1007/JHEP12(2010)032 |
| [123] | Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B425 (1994) 217 [hep-ph/9403226] [INSPIRE]. · Zbl 1049.81644 |
| [124] | Brandhuber, A.; Spence, BJ; Travaglini, G., One-loop gauge theory amplitudes in N = 4 super Yang-Mills from MHV vertices, Nucl. Phys. B, 706, 150 (2005) · Zbl 1119.81363 · doi:10.1016/j.nuclphysb.2004.11.023 |
| [125] | L.S. Brown and D.B. Creamer, Vacuum polarization about instantons, Phys. Rev. D18 (1978) 3695 [INSPIRE]. |
| [126] | E. Corrigan, P. Goddard, H. Osborn and S. Templeton, Zeta function regularization and multi-instanton determinants, Nucl. Phys. B159 (1979) 469 [INSPIRE]. |
| [127] | W.A. Bardeen, Selfdual Yang-Mills theory, integrability and multiparton amplitudes, Prog. Theor. Phys. Suppl.123 (1996) 1 [INSPIRE]. |
| [128] | K.J. Costello, Quantizing local holomorphic field theories on twistor space, arXiv:2111.08879 [INSPIRE]. |
| [129] | R. Monteiro, R. Stark-Muchão and S. Wikeley, Anomaly and double copy in quantum self-dual Yang-Mills and gravity, arXiv:2211.12407 [INSPIRE]. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
