Abstract
We study the consistency conditions for interactions of massless fields of any spin in four-dimensional flat space using the light-cone approach. We show that they can be equivalently rewritten as the Ward identities for the off-shell light-cone amplitudes built from the light-cone Hamiltonian in the standard way. Then we find a general solution of these Ward identities. The solution admits a compact representation when written in the spinor-helicity form and is given by an arbitrary function of spinor products, satisfying wellknown homogeneity constraints. Thus, we show that the light-cone consistent deformation procedure inevitably leads to a certain off-shell version of the spinor-helicity approach. We discuss how the relation between the two approaches can be employed to facilitate the search of consistent interaction of massless higher-spin fields.
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References
E.P. Wigner, On Unitary Representations of the Inhomogeneous Lorentz Group, Annals Math. 40 (1939) 149 [Nucl. Phys. Proc. Suppl. 6 (1989) 9].
X. Bekaert and N. Boulanger, The Unitary representations of the Poincaré group in any spacetime dimension, hep-th/0611263 [INSPIRE].
C. Aragone and S. Deser, Consistency Problems of Hypergravity, Phys. Lett. B 86 (1979) 161 [INSPIRE].
X. Bekaert, N. Boulanger and S. Leclercq, Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex, J. Phys. A 43 (2010) 185401 [arXiv:1002.0289] [INSPIRE].
E. Joung and M. Taronna, Cubic-interaction-induced deformations of higher-spin symmetries, JHEP 03 (2014) 103 [arXiv:1311.0242] [INSPIRE].
S. Weinberg, Photons and Gravitons in s Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass, Phys. Rev. 135 (1964) B1049.
S.R. Coleman and J. Mandula, All Possible Symmetries of the S Matrix, Phys. Rev. 159 (1967) 1251 [INSPIRE].
X. Bekaert, N. Boulanger and P. Sundell, How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples, Rev. Mod. Phys. 84 (2012) 987 [arXiv:1007.0435] [INSPIRE].
A.K.H. Bengtsson, I. Bengtsson and L. Brink, Cubic Interaction Terms for Arbitrary Spin, Nucl. Phys. B 227 (1983) 31 [INSPIRE].
A.K.H. Bengtsson, I. Bengtsson and L. Brink, Cubic Interaction Terms for Arbitrarily Extended Supermultiplets, Nucl. Phys. B 227 (1983) 41 [INSPIRE].
A.K.H. Bengtsson, I. Bengtsson and N. Linden, Interacting Higher Spin Gauge Fields on the Light Front, Class. Quant. Grav. 4 (1987) 1333 [INSPIRE].
E. Conde, E. Joung and K. Mkrtchyan, Spinor-Helicity Three-Point Amplitudes from Local Cubic Interactions, JHEP 08 (2016) 040 [arXiv:1605.07402] [INSPIRE].
C. Sleight and M. Taronna, Higher-Spin Algebras, Holography and Flat Space, arXiv:1609.00991 [INSPIRE].
R.R. Metsaev, Poincaré invariant dynamics of massless higher spins: Fourth order analysis on mass shell, Mod. Phys. Lett. A 6 (1991) 359 [INSPIRE].
R.R. Metsaev, S matrix approach to massless higher spins theory. 2: The Case of internal symmetry, Mod. Phys. Lett. A 6 (1991) 2411 [INSPIRE].
R.R. Metsaev, Generating function for cubic interaction vertices of higher spin fields in any dimension, Mod. Phys. Lett. A 8 (1993) 2413 [INSPIRE].
A.K.H. Bengtsson, A Riccati type PDE for light-front higher helicity vertices, JHEP 09 (2014) 105 [arXiv:1403.7345] [INSPIRE].
N. Boulanger and S. Leclercq, Consistent couplings between spin-2 and spin-3 massless fields, JHEP 11 (2006) 034 [hep-th/0609221] [INSPIRE].
D. Ponomarev and E.D. Skvortsov, Light-Front Higher-Spin Theories in Flat Space, arXiv:1609.04655 [INSPIRE].
S. Ananth, Spinor helicity structures in higher spin theories, JHEP 11 (2012) 089 [arXiv:1209.4960] [INSPIRE].
Y.S. Akshay and S. Ananth, Factorization of cubic vertices involving three different higher spin fields, Nucl. Phys. B 887 (2014) 168 [arXiv:1404.2448] [INSPIRE].
P. Benincasa and F. Cachazo, Consistency Conditions on the S-matrix of Massless Particles, arXiv:0705.4305 [INSPIRE].
A.K.H. Bengtsson, Notes on Cubic and Quartic Light-Front Kinematics, arXiv:1604.01974 [INSPIRE].
A.K.H. Bengtsson, Quartic amplitudes for Minkowski higher spin, arXiv:1605.02608 [INSPIRE].
G. Chalmers and W. Siegel, Simplifying algebra in Feynman graphs. Part 2. Spinor helicity from the space-cone, Phys. Rev. D 59 (1999) 045013 [hep-ph/9801220] [INSPIRE].
T. Heinzl, Light cone quantization: Foundations and applications, Lect. Notes Phys. 572 (2001) 55 [hep-th/0008096] [INSPIRE].
P.A.M. Dirac, Forms of Relativistic Dynamics, Rev. Mod. Phys. 21 (1949) 392 [INSPIRE].
J.B. Kogut and D.E. Soper, Quantum Electrodynamics in the Infinite Momentum Frame, Phys. Rev. D 1 (1970) 2901 [INSPIRE].
A.K.H. Bengtsson, Investigations into Light-front Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes, arXiv:1607.06659 [INSPIRE].
L.J. Dixon, Calculating scattering amplitudes efficiently, in Proceedings of Theoretical Advanced Study Institute in Elementary Particle Physics, TASI-95: QCD and Beyond, Boulder U.S.A. (1995), pg. 539 [hep-ph/9601359] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, On-Shell Methods in Perturbative QCD, Annals Phys. 322 (2007) 1587 [arXiv:0704.2798] [INSPIRE].
H. Elvang and Y.-t. Huang, Scattering Amplitudes, arXiv:1308.1697 [INSPIRE].
W.A. Bardeen, Selfdual Yang-Mills theory, integrability and multiparton amplitudes, Prog. Theor. Phys. Suppl. 123 (1996) 1 [INSPIRE].
D. Cangemi, Self-dual Yang-Mills theory and one-loop maximally helicity violating multi-gluon amplitudes, Nucl. Phys. B 484 (1997) 521 [hep-th/9605208] [INSPIRE].
F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [INSPIRE].
A. Gorsky and A. Rosly, From Yang-Mills Lagrangian to MHV diagrams, JHEP 01 (2006) 101 [hep-th/0510111] [INSPIRE].
P. Mansfield, The Lagrangian origin of MHV rules, JHEP 03 (2006) 037 [hep-th/0511264] [INSPIRE].
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].
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].
P. Benincasa and E. Conde, On the Tree-Level Structure of Scattering Amplitudes of Massless Particles, JHEP 11 (2011) 074 [arXiv:1106.0166] [INSPIRE].
P. Benincasa and E. Conde, Exploring the S-matrix of Massless Particles, Phys. Rev. D 86 (2012) 025007 [arXiv:1108.3078] [INSPIRE].
D.A. McGady and L. Rodina, Higher-spin massless S-matrices in four-dimensions, Phys. Rev. D 90 (2014) 084048 [arXiv:1311.2938] [INSPIRE].
X. Bekaert, J. Erdmenger, D. Ponomarev and C. Sleight, Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory, JHEP 11 (2015) 149 [arXiv:1508.04292] [INSPIRE].
G. Barnich and M. Henneaux, Consistent couplings between fields with a gauge freedom and deformations of the master equation, Phys. Lett. B 311 (1993) 123 [hep-th/9304057] [INSPIRE].
A. Fotopoulos and M. Tsulaia, On the Tensionless Limit of String theory, Off-Shell Higher Spin Interaction Vertices and BCFW Recursion Relations, JHEP 11 (2010) 086 [arXiv:1009.0727] [INSPIRE].
D. Ponomarev and A.A. Tseytlin, On quantum corrections in higher-spin theory in flat space, JHEP 05 (2016) 184 [arXiv:1603.06273] [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].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
E. Conde and A. Marzolla, Lorentz Constraints on Massive Three-Point Amplitudes, JHEP 09 (2016) 041 [arXiv:1601.08113] [INSPIRE].
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Ponomarev, D. Off-shell spinor-helicity amplitudes from light-cone deformation procedure. J. High Energ. Phys. 2016, 117 (2016). https://doi.org/10.1007/JHEP12(2016)117
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DOI: https://doi.org/10.1007/JHEP12(2016)117