Wilson lines, Grassmannians and gauge invariant off-shell amplitudes in \( \mathcal{N}=4 \) SYM. (English) Zbl 1378.81135
Summary: In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in \( \mathcal{N}=4 \) SYM. For the off-shell amplitudes with one leg off-shell we present a conjecture for their Grassmannian integral representation in spinor helicity, twistor and momentum twistor parameterizations. The presented conjecture is successfully checked against BCFW results for \(MHV_n\), \(NMHV_4\) and \(NMHV_5\) off-shell amplitudes. We have also verified that our Grassmannian integral representation correctly reproduces soft (on-shell) limit for the off-shell gluon momentum. It is shown that the (deformed) off-shell amplitude expressions could be also obtained using quantum inverse scattering method for auxiliary \( \mathfrak{g}\mathfrak{l}\left(4 | 4\right) \) super spin chain.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81U15 | Exactly and quasi-solvable systems arising in quantum theory |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
Software:
positroidsReferences:
| [1] | Z. Bern, L.J. Dixon and D.A. Kosower, Progress in one loop QCD computations, Ann. Rev. Nucl. Part. Sci.46 (1996) 109 [hep-ph/9602280] [INSPIRE]. · Zbl 1122.81077 |
| [2] | Z. Bern, L.J. Dixon and D.A. Kosower, On-shell methods in perturbative QCD, Annals Phys.322 (2007) 1587 [arXiv:0704.2798] [INSPIRE]. · Zbl 1122.81077 |
| [3] | R. Britto, Loop amplitudes in gauge theories: modern analytic approaches, J. Phys.A 44 (2011) 454006 [arXiv:1012.4493] [INSPIRE]. · Zbl 1270.81132 |
| [4] | Z. Bern and Y.-t. Huang, Basics of generalized unitarity, J. Phys.A 44 (2011) 454003 [arXiv:1103.1869] [INSPIRE]. · Zbl 1270.81209 |
| [5] | H. Elvang and Y.-t. Huang, Scattering amplitudes, arXiv:1308.1697 [INSPIRE]. · Zbl 1332.81010 |
| [6] | R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys.B 715 (2005) 499 [hep-th/0412308] [INSPIRE]. · Zbl 1207.81088 |
| [7] | R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett.94 (2005) 181602 [hep-th/0501052] [INSPIRE]. |
| [8] | A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, JHEP05 (2013) 135 [arXiv:0905.1473] [INSPIRE]. · Zbl 1342.81291 |
| [9] | V.P. Nair, A current algebra for some gauge theory amplitudes, Phys. Lett.B 214 (1988) 215 [INSPIRE]. |
| [10] | J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys.B 828 (2010) 317 [arXiv:0807.1095] [INSPIRE]. · Zbl 1203.81112 |
| [11] | E.A. Ivanov, Gauge fields, nonlinear realizations, supersymmetry, Phys. Part. Nucl.47 (2016) 508 [arXiv:1604.01379] [INSPIRE]. |
| [12] | J.M. Drummond, J.M. Henn and J. Plefka, Yangian symmetry of scattering amplitudes in N = 4 super Yang-Mills theory, JHEP05 (2009) 046 [arXiv:0902.2987] [INSPIRE]. |
| [13] | N. Beisert, On Yangian symmetry in planar N = 4 SYM, arXiv:1004.5423 [INSPIRE]. |
| [14] | N. Beisert, J. Broedel and M. Rosso, On Yangian-invariant regularization of deformed on-shell diagrams \[inN=4 \mathcal{N}=4\] super-Yang-Mills theory, J. Phys.A 47 (2014) 365402 [arXiv:1401.7274] [INSPIRE]. · Zbl 1298.81339 |
| [15] | L. Ferro, T. Lukowski, C. Meneghelli, J. Plefka and M. Staudacher, Harmonic R-matrices for scattering amplitudes and spectral regularization, Phys. Rev. Lett.110 (2013) 121602 [arXiv:1212.0850] [INSPIRE]. · Zbl 1333.81398 |
| [16] | L. Ferro, T. Lukowski, C. Meneghelli, J. Plefka and M. Staudacher, Spectral parameters for scattering amplitudes in N = 4 Super Yang-Mills theory, JHEP01 (2014) 094 [arXiv:1308.3494] [INSPIRE]. · Zbl 1333.81398 |
| [17] | D. Chicherin, S. Derkachov and R. Kirschner, Yang-Baxter operators and scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys.B 881 (2014) 467 [arXiv:1309.5748] [INSPIRE]. · Zbl 1284.81276 |
| [18] | R. Frassek, N. Kanning, Y. Ko and M. Staudacher, Bethe ansatz for Yangian invariants: towards super Yang-Mills scattering amplitudes, Nucl. Phys.B 883 (2014) 373 [arXiv:1312.1693] [INSPIRE]. · Zbl 1323.81058 |
| [19] | N. Kanning, T. Lukowski and M. Staudacher, A shortcut to general tree-level scattering amplitudes \[inN=4 \mathcal{N}=4\] SYM via integrability, Fortsch. Phys.62 (2014) 556 [arXiv:1403.3382] [INSPIRE]. · Zbl 1338.81289 |
| [20] | J. Broedel, M. de Leeuw and M. Rosso, A dictionary between R-operators, on-shell graphs and Yangian algebras, JHEP06 (2014) 170 [arXiv:1403.3670] [INSPIRE]. · Zbl 1333.81159 |
| [21] | J. Broedel, M. de Leeuw and M. Rosso, Deformed one-loop amplitudes \[inN=4 \mathcal{N}=4\] super-Yang-Mills theory, JHEP11 (2014) 091 [arXiv:1406.4024] [INSPIRE]. · Zbl 1333.81232 |
| [22] | N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A duality for the S matrix, JHEP03 (2010) 020 [arXiv:0907.5418] [INSPIRE]. · Zbl 1271.81098 |
| [23] | N. Arkani-Hamed et al., Scattering amplitudes and the positive grassmannian, arXiv:1212.5605. · Zbl 0391.76060 |
| [24] | N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The all-loop integrand for scattering amplitudes in planar N = 4 SYM, JHEP01 (2011) 041 [arXiv:1008.2958] [INSPIRE]. · Zbl 1214.81141 |
| [25] | N. Arkani-Hamed, F. Cachazo and C. Cheung, The Grassmannian origin of dual superconformal invariance, JHEP03 (2010) 036 [arXiv:0909.0483] [INSPIRE]. · Zbl 1271.81099 |
| [26] | N. Arkani-Hamed, J. Bourjaily, F. Cachazo and J. Trnka, Unification of residues and grassmannian dualities, JHEP01 (2011) 049 [arXiv:0912.4912] [INSPIRE]. · Zbl 1214.81267 |
| [27] | L.J. Mason and D. Skinner, Dual superconformal invariance, momentum twistors and Grassmannians, JHEP11 (2009) 045 [arXiv:0909.0250] [INSPIRE]. |
| [28] | J.M. Drummond and L. Ferro, Yangians, Grassmannians and T-duality, JHEP07 (2010) 027 [arXiv:1001.3348] [INSPIRE]. · Zbl 1290.81062 |
| [29] | J.M. Drummond and L. Ferro, The Yangian origin of the Grassmannian integral, JHEP12 (2010) 010 [arXiv:1002.4622] [INSPIRE]. · Zbl 1294.81101 |
| [30] | N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, A. Hodges and J. Trnka, A note on polytopes for scattering amplitudes, JHEP04 (2012) 081 [arXiv:1012.6030] [INSPIRE]. · Zbl 1348.81339 |
| [31] | N. Arkani-Hamed and J. Trnka, The amplituhedron, JHEP10 (2014) 030 [arXiv:1312.2007] [INSPIRE]. · Zbl 1468.81075 |
| [32] | N. Arkani-Hamed and J. Trnka, Into the amplituhedron, JHEP12 (2014) 182 [arXiv:1312.7878] [INSPIRE]. |
| [33] | Y. Bai and S. He, The amplituhedron from momentum twistor diagrams, JHEP02 (2015) 065 [arXiv:1408.2459] [INSPIRE]. · Zbl 1388.81230 |
| [34] | S. Franco, D. Galloni, A. Mariotti and J. Trnka, Anatomy of the amplituhedron, JHEP03 (2015) 128 [arXiv:1408.3410] [INSPIRE]. · Zbl 1388.81718 |
| [35] | Z. Bern, E. Herrmann, S. Litsey, J. Stankowicz and J. Trnka, Evidence for a nonplanar amplituhedron, JHEP06 (2016) 098 [arXiv:1512.08591] [INSPIRE]. · Zbl 1388.81908 |
| [36] | L. Ferro, T. Lukowski, A. Orta and M. Parisi, Towards the amplituhedron volume, JHEP03 (2016) 014 [arXiv:1512.04954] [INSPIRE]. · Zbl 1388.81315 |
| [37] | A. Brandhuber, B. Spence, G. Travaglini and G. Yang, Form factors in N = 4 Super Yang-Mills and periodic Wilson loops, JHEP01 (2011) 134 [arXiv:1011.1899] [INSPIRE]. · Zbl 1214.81146 |
| [38] | A. Brandhuber, O. Gurdogan, R. Mooney, G. Travaglini and G. Yang, Harmony of super form factors, JHEP10 (2011) 046 [arXiv:1107.5067] [INSPIRE]. · Zbl 1303.81111 |
| [39] | L.V. Bork, On NMHV form factors in N = 4 SYM theory from generalized unitarity, JHEP01 (2013) 049 [arXiv:1203.2596] [INSPIRE]. · Zbl 1342.81555 |
| [40] | A. Brandhuber, G. Travaglini and G. Yang, Analytic two-loop form factors in N = 4 SYM, JHEP05 (2012) 082 [arXiv:1201.4170] [INSPIRE]. · Zbl 1348.81400 |
| [41] | O.T. Engelund and R. Roiban, Correlation functions of local composite operators from generalized unitarity, JHEP03 (2013) 172 [arXiv:1209.0227] [INSPIRE]. · Zbl 1342.81278 |
| [42] | B. Penante, B. Spence, G. Travaglini and C. Wen, On super form factors of half-BPS operators in N = 4 super Yang-Mills, JHEP04 (2014) 083 [arXiv:1402.1300] [INSPIRE]. |
| [43] | A. Brandhuber, B. Penante, G. Travaglini and C. Wen, The last of the simple remainders, JHEP08 (2014) 100 [arXiv:1406.1443] [INSPIRE]. |
| [44] | L.V. Bork, On form factors \[inN=4 \mathcal{N}=4\] SYM theory and polytopes, JHEP12 (2014) 111 [arXiv:1407.5568] [INSPIRE]. |
| [45] | M. Wilhelm, Amplitudes, form factors and the dilatation operator \[inN=4 \mathcal{N}=4\] SYM theory, JHEP02 (2015) 149 [arXiv:1410.6309] [INSPIRE]. · Zbl 1388.81427 |
| [46] | D. Nandan, C. Sieg, M. Wilhelm and G. Yang, Cutting through form factors and cross sections of non-protected operators \[inN=4 \mathcal{N}=4\] SYM, JHEP06 (2015) 156 [arXiv:1410.8485] [INSPIRE]. · Zbl 1388.81393 |
| [47] | M. Wilhelm, Form factors and the dilatation operator \[inN=4 \mathcal{N}=4\] super Yang-Mills theory and its deformations, arXiv:1603.01145 [INSPIRE]. · Zbl 1388.81427 |
| [48] | F. Loebbert, D. Nandan, C. Sieg, M. Wilhelm and G. Yang, On-shell methods for the two-loop dilatation operator and finite remainders, JHEP10 (2015) 012 [arXiv:1504.06323] [INSPIRE]. · Zbl 1388.81390 |
| [49] | L. Koster, V. Mitev, M. Staudacher and M. Wilhelm, All tree-level MHV form factors \[inN=4 \mathcal{N}=4\] SYM from twistor space, JHEP06 (2016) 162 [arXiv:1604.00012] [INSPIRE]. · Zbl 1388.81338 |
| [50] | L. Koster, V. Mitev, M. Staudacher and M. Wilhelm, Composite operators in the twistor formulation of N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett.117 (2016) 011601 [arXiv:1603.04471] [INSPIRE]. |
| [51] | D. Chicherin and E. Sokatchev, \[N=4 \mathcal{N}=4\] super-Yang-Mills in LHC superspace part I: classical and quantum theory, JHEP02 (2017) 062 [arXiv:1601.06803] [INSPIRE]. · Zbl 1377.83026 |
| [52] | D. Chicherin and E. Sokatchev, \[N=4 \mathcal{N}=4\] super-Yang-Mills in LHC superspace part II: non-chiral correlation functions of the stress-tensor multiplet, JHEP03 (2017) 048 [arXiv:1601.06804] [INSPIRE]. · Zbl 1377.83133 |
| [53] | D. Chicherin and E. Sokatchev, Composite operators and form factors in N = 4 SYM, arXiv:1605.01386 [INSPIRE]. · Zbl 1370.81114 |
| [54] | R. Huang, Q. Jin and B. Feng, Form factor and boundary contribution of amplitude, JHEP06 (2016) 072 [arXiv:1601.06612] [INSPIRE]. · Zbl 1388.81835 |
| [55] | J.M. Henn, S. Moch and S.G. Naculich, Form factors and scattering amplitudes in N = 4 SYM in dimensional and massive regularizations, JHEP12 (2011) 024 [arXiv:1109.5057] [INSPIRE]. · Zbl 1306.81111 |
| [56] | T. Gehrmann, J.M. Henn and T. Huber, The three-loop form factor in N = 4 super Yang-Mills, JHEP03 (2012) 101 [arXiv:1112.4524] [INSPIRE]. · Zbl 1309.81159 |
| [57] | R.H. Boels, B.A. Kniehl, O.V. Tarasov and G. Yang, Color-kinematic duality for form factors, JHEP02 (2013) 063 [arXiv:1211.7028] [INSPIRE]. · Zbl 1342.81551 |
| [58] | R. Boels, B.A. Kniehl and G. Yang, Master integrals for the four-loop Sudakov form factor, Nucl. Phys.B 902 (2016) 387 [arXiv:1508.03717] [INSPIRE]. · Zbl 1332.81126 |
| [59] | O.T. Engelund, Lagrangian insertion in the light-like limit and the super-correlators/super-amplitudes duality, JHEP02 (2016) 030 [arXiv:1502.01934] [INSPIRE]. · Zbl 1388.81808 |
| [60] | A. Brandhuber, M. Kostacinska, B. Penante, G. Travaglini and D. Young, The SU(2|3) dynamic two-loop form factors, JHEP08 (2016) 134 [arXiv:1606.08682] [INSPIRE]. · Zbl 1390.81306 |
| [61] | L.V. Bork and A.I. Onishchenko, On soft theorems and form factors \[inN=4 \mathcal{N}=4\] SYM theory, JHEP12 (2015) 030 [arXiv:1506.07551] [INSPIRE]. |
| [62] | R. Frassek, D. Meidinger, D. Nandan and M. Wilhelm, On-shell diagrams, Graßmannians and integrability for form factors, JHEP01 (2016) 182 [arXiv:1506.08192] [INSPIRE]. · Zbl 1388.81209 |
| [63] | L.V. Bork and A.I. Onishchenko, Grassmannians and form factors with \[q2 = 0 inN=4 \mathcal{N}=4\] SYM theory, JHEP12 (2016) 076 [arXiv:1607.00503] [INSPIRE]. · Zbl 1390.81566 |
| [64] | A. van Hameren, BCFW recursion for off-shell gluons, JHEP07 (2014) 138 [arXiv:1404.7818] [INSPIRE]. |
| [65] | L.N. Lipatov, Gauge invariant effective action for high-energy processes in QCD, Nucl. Phys.B 452 (1995) 369 [hep-ph/9502308] [INSPIRE]. · Zbl 1342.81555 |
| [66] | L.N. Lipatov, Small x physics in perturbative QCD, Phys. Rept.286 (1997) 131 [hep-ph/9610276] [INSPIRE]. |
| [67] | E.N. Antonov, L.N. Lipatov, E.A. Kuraev and I.O. Cherednikov, Feynman rules for effective Regge action, Nucl. Phys.B 721 (2005) 111 [hep-ph/0411185] [INSPIRE]. · Zbl 1128.81314 |
| [68] | R. Kirschner, L.N. Lipatov and L. Szymanowski, Effective action for multi-Regge processes in QCD, Nucl. Phys.B 425 (1994) 579 [hep-th/9402010] [INSPIRE]. |
| [69] | R. Kirschner, L.N. Lipatov and L. Szymanowski, Symmetry properties of the effective action for high-energy scattering in QCD, Phys. Rev.D 51 (1995) 838 [hep-th/9403082] [INSPIRE]. |
| [70] | P. Kotko, Wilson lines and gauge invariant off-shell amplitudes, JHEP07 (2014) 128 [arXiv:1403.4824] [INSPIRE]. |
| [71] | A. van Hameren, P. Kotko and K. Kutak, Multi-gluon helicity amplitudes with one off-shell leg within high energy factorization, JHEP12 (2012) 029 [arXiv:1207.3332] [INSPIRE]. |
| [72] | A. van Hameren, P. Kotko and K. Kutak, Helicity amplitudes for high-energy scattering, JHEP01 (2013) 078 [arXiv:1211.0961] [INSPIRE]. |
| [73] | A. van Hameren and M. Serino, BCFW recursion for TMD parton scattering, JHEP07 (2015) 010 [arXiv:1504.00315] [INSPIRE]. |
| [74] | L.V. Gribov, E.M. Levin and M.G. Ryskin, Semihard processes in QCD, Phys. Rept.100 (1983) 1 [INSPIRE]. |
| [75] | S. Catani, M. Ciafaloni and F. Hautmann, High-energy factorization and small x heavy flavor production, Nucl. Phys.B 366 (1991) 135 [INSPIRE]. |
| [76] | J.C. Collins and R.K. Ellis, Heavy quark production in very high-energy hadron collisions, Nucl. Phys.B 360 (1991) 3 [INSPIRE]. |
| [77] | S. Catani and F. Hautmann, High-energy factorization and small x deep inelastic scattering beyond leading order, Nucl. Phys.B 427 (1994) 475 [hep-ph/9405388] [INSPIRE]. |
| [78] | F.A. Berends and W.T. Giele, Recursive calculations for processes with n gluons, Nucl. Phys.B 306 (1988) 759 [INSPIRE]. |
| [79] | D.A. Kosower, Light cone recurrence relations for QCD amplitudes, Nucl. Phys.B 335 (1990) 23 [INSPIRE]. |
| [80] | B. Feng and Z. Zhang, Boundary Contributions Using Fermion Pair Deformation, JHEP12 (2011) 057 [arXiv:1109.1887] [INSPIRE]. · Zbl 1306.81101 |
| [81] | C.-H. Fu and R. Kallosh, New N = 4 SYM path integral, Phys. Rev.D 82 (2010) 125022 [arXiv:1005.4171] [INSPIRE]. |
| [82] | J. Broedel and R. Kallosh, From lightcone actions to maximally supersymmetric amplitudes, JHEP06 (2011) 024 [arXiv:1103.0322] [INSPIRE]. · Zbl 1298.81161 |
| [83] | L.J. Dixon, Calculating scattering amplitudes efficiently, in the proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI-95), June 4-30, Boulder, U.S.A. (1995), hep-ph/9601359 [INSPIRE]. |
| [84] | L.V. Bork, D.I. Kazakov and G.S. Vartanov, On form factors in N = 4 SYM, JHEP02 (2011) 063 [arXiv:1011.2440] [INSPIRE]. · Zbl 1294.81090 |
| [85] | L.V. Bork, D.I. Kazakov and G.S. Vartanov, On MHV form factors in superspace \[forN=4 \mathcal{N}=4\] SYM theory, JHEP10 (2011) 133 [arXiv:1107.5551] [INSPIRE]. · Zbl 1303.81110 |
| [86] | J. Maldacena and A. Zhiboedov, Form factors at strong coupling via a Y-system, JHEP11 (2010) 104 [arXiv:1009.1139] [INSPIRE]. · Zbl 1294.81121 |
| [87] | Z. Gao and G. Yang, Y-system for form factors at strong coupling in AdS5and with multi-operator insertions in AdS3, JHEP06 (2013) 105 [arXiv:1303.2668] [INSPIRE]. |
| [88] | H. Ooguri, J. Rahmfeld, H. Robins and J. Tannenhauser, Holography in superspace, JHEP07 (2000) 045 [hep-th/0007104] [INSPIRE]. · Zbl 0965.81070 |
| [89] | D. Müller, H. Münkler, J. Plefka, J. Pollok and K. Zarembo, Yangian symmetry of smooth Wilson Loops \[inN=4 \mathcal{N}=4\] super Yang-Mills theory, JHEP11 (2013) 081 [arXiv:1309.1676] [INSPIRE]. · Zbl 1342.81312 |
| [90] | N. Beisert, D. Müller, J. Plefka and C. Vergu, Smooth Wilson loops \[inN=4 \mathcal{N}=4\] non-chiral superspace, JHEP12 (2015) 140 [arXiv:1506.07047] [INSPIRE]. · Zbl 1388.81631 |
| [91] | J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett.80 (1998) 4859 [hep-th/9803002] [INSPIRE]. · Zbl 0947.81128 |
| [92] | S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and Anti-de Sitter supergravity, Eur. Phys. J.C 22 (2001) 379 [hep-th/9803001] [INSPIRE]. · Zbl 1072.81555 |
| [93] | L.J. Mason and D. Skinner, The complete planar S-matrix of N = 4 SYM as a Wilson loop in twistor space, JHEP12 (2010) 018 [arXiv:1009.2225] [INSPIRE]. · Zbl 1294.81122 |
| [94] | S. Caron-Huot, Notes on the scattering amplitude/Wilson loop duality, JHEP07 (2011) 058 [arXiv:1010.1167] [INSPIRE]. · Zbl 1298.81357 |
| [95] | N. Beisert, S. He, B.U.W. Schwab and C. Vergu, Null polygonal Wilson loops in full N = 4 superspace, J. Phys.A 45 (2012) 265402 [arXiv:1203.1443] [INSPIRE]. · Zbl 1258.81075 |
| [96] | A. Brandhuber, P. Heslop and G. Travaglini, A note on dual superconformal symmetry of the N = 4 super Yang-Mills S-matrix, Phys. Rev.D 78 (2008) 125005 [arXiv:0807.4097] [INSPIRE]. |
| [97] | N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP09 (2010) 016 [arXiv:0808.1446] [INSPIRE]. · Zbl 1291.81356 |
| [98] | S. Franco, D. Galloni, B. Penante and C. Wen, Non-planar on-shell diagrams, JHEP06 (2015) 199 [arXiv:1502.02034] [INSPIRE]. · Zbl 1388.81148 |
| [99] | A. Postnikov, Total positivity, Grassmannians and networks, math/0609764 [INSPIRE]. |
| [100] | S. Franco, Bipartite field theories: from D-brane probes to scattering amplitudes, JHEP11 (2012) 141 [arXiv:1207.0807] [INSPIRE]. · Zbl 1397.81239 |
| [101] | J.L. Bourjaily, Positroids, Plabic graphs and scattering amplitudes in Mathematica, arXiv:1212.6974 [INSPIRE]. |
| [102] | E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys.252 (2004) 189 [hep-th/0312171] [INSPIRE]. · Zbl 1105.81061 |
| [103] | H. Elvang et al., Grassmannians for scattering amplitudes in \[4dN=4 \mathcal{N}=4\] SYM and 3d ABJM, JHEP12 (2014) 181 [arXiv:1410.0621] [INSPIRE]. |
| [104] | J. Rao, Soft theorem \[ofN=4 \mathcal{N}=4\] SYM in Grassmannian formulation, JHEP02 (2015) 087 [arXiv:1410.5047] [INSPIRE]. |
| [105] | F. Gliozzi, J. Scherk and D.I. Olive, Supersymmetry, supergravity theories and the dual spinor model, Nucl. Phys.B 122 (1977) 253 [INSPIRE]. |
| [106] | L. Brink, J.H. Schwarz and J. Scherk, Supersymmetric Yang-Mills theories, Nucl. Phys.B 121 (1977) 77 [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.
