Abstract
We use on-shell Supersymmetry to constrain the three-point function of two massless particles and one massive particle in 3+1 dimensions. We use this information to write down the tree-level four-point function of massless particles for \( \mathcal{N} \) = 1, 2 and 4 theories. In particular, we derive the expressions for four-photon/gluon amplitudes with massive higher spin exchange in theories with \( \mathcal{N} \) = 4 Supersymmetry in 3+1 dimensions.
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R. Rahman, Higher Spin Theory. Part I, PoS ModaveVIII (2012) 004 [arXiv:1307.3199] [INSPIRE].
D. Ponomarev, Basic introduction to higher-spin theories, arXiv:2206.15385.
X. Bekaert et al., Snowmass White Paper: Higher Spin Gravity and Higher Spin Symmetry, arXiv:2205.01567.
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
P. Maity, Positivity of the Veneziano amplitude in D = 4, JHEP 04 (2022) 064 [arXiv:2110.01578] [INSPIRE].
N. Arkani-Hamed, L. Eberhardt, Y.-T. Huang and S. Mizera, On unitarity of tree-level string amplitudes, JHEP 02 (2022) 197 [arXiv:2201.11575] [INSPIRE].
S. Chakraborty, S.D. Chowdhury, T. Gopalka, S. Kundu, S. Minwalla and A. Mishra, Classification of all 3 particle S-matrices quadratic in photons or gravitons, JHEP 04 (2020) 110 [arXiv:2001.07117] [INSPIRE].
M.K.N. Balasubramanian, R. Patil and A. Rudra, Spinning amplitudes from scalar amplitudes, JHEP 11 (2021) 151 [arXiv:2106.05301] [INSPIRE].
S.R. Coleman and J. Mandula, All Possible Symmetries of the S Matrix, Phys. Rev. 159 (1967) 1251 [INSPIRE].
A. Herderschee, S. Koren and T. Trott, Massive On-Shell Supersymmetric Scattering Amplitudes, JHEP 10 (2019) 092 [arXiv:1902.07204] [INSPIRE].
A. Herderschee, S. Koren and T. Trott, Constructing \( \mathcal{N} \) = 4 Coulomb branch superamplitudes, JHEP 08 (2019) 107 [arXiv:1902.07205].
L. Engelbrecht, C.R.T. Jones and S. Paranjape, Supersymmetric Massive Gravity, JHEP 10 (2022) 130 [arXiv:2205.12982] [INSPIRE].
M. Chiodaroli, M. Gunaydin, H. Johansson and R. Roiban, Spinor-helicity formalism for massive and massless amplitudes in five dimensions, JHEP 02 (2023) 040 [arXiv:2202.08257] [INSPIRE].
M. Abhishek, S. Hegde, D.P. Jatkar and A.P. Saha, Scattering Amplitudes and BCFW in \( \mathcal{N} \) = 2* Theory, SciPost Phys. 13 (2022) 008 [arXiv:2202.12204].
J.-Y. Liu and Z.-M. You, The supersymmetric spinning polynomial, arXiv:2011.11299.
L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, Scattering Amplitudes For All Masses and Spins, arXiv:1709.04891.
E. Conde and A. Marzolla, Lorentz Constraints on Massive Three-Point Amplitudes, JHEP 09 (2016) 041 [arXiv:1601.08113] [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].
S.D. Chowdhury, A. Gadde, T. Gopalka, I. Halder, L. Janagal and S. Minwalla, Classifying and constraining local four photon and four graviton S-matrices, JHEP 02 (2020) 114 [arXiv:1910.14392] [INSPIRE].
S. De Angelis, Amplitude bases in generic EFTs, JHEP 08 (2022) 299 [arXiv:2202.02681] [INSPIRE].
A. Salam and J.A. Strathdee, Supersymmetry and Superfields, Fortsch. Phys. 26 (1978) 57.
H. Elvang and Y.-T. Huang, Scattering Amplitudes in Gauge Theory and Gravity, Cambridge University Press (2015).
M. Bianchi, H. Elvang and D.Z. Freedman, Generating Tree Amplitudes in N = 4 SYM and N = 8 SG, JHEP 09 (2008) 063 [arXiv:0805.0757] [INSPIRE].
H. Elvang, D.Z. Freedman and M. Kiermaier, Recursion Relations, Generating Functions, and Unitarity Sums in N = 4 SYM Theory, JHEP 04 (2009) 009 [arXiv:0808.1720] [INSPIRE].
H. Elvang, D.Z. Freedman and M. Kiermaier, Proof of the MHV vertex expansion for all tree amplitudes in N = 4 SYM theory, JHEP 06 (2009) 068 [arXiv:0811.3624] [INSPIRE].
H. Elvang, D.Z. Freedman and M. Kiermaier, Solution to the Ward Identities for Superamplitudes, JHEP 10 (2010) 103 [arXiv:0911.3169] [INSPIRE].
H. Elvang, D.Z. Freedman and M. Kiermaier, SUSY Ward identities, Superamplitudes, and Counterterms, J. Phys. A 44 (2011) 454009 [arXiv:1012.3401] [INSPIRE].
Z. Bern, D. Kosmopoulos and A. Zhiboedov, Gravitational effective field theory islands, low-spin dominance, and the four-graviton amplitude, J. Phys. A 54 (2021) 344002 [arXiv:2103.12728] [INSPIRE].
Z. Bern, E. Herrmann, D. Kosmopoulos and R. Roiban, Effective Field Theory islands from perturbative and nonperturbative four-graviton amplitudes, JHEP 01 (2023) 113 [arXiv:2205.01655] [INSPIRE].
S. Pasterski, S.-H. Shao and A. Strominger, Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere, Phys. Rev. D 96 (2017) 065026 [arXiv:1701.00049] [INSPIRE].
S. Pasterski and A. Puhm, Shifting spin on the celestial sphere, Phys. Rev. D 104 (2021) 086020 [arXiv:2012.15694] [INSPIRE].
S. Pasterski, M. Pate and A.-M. Raclariu, Celestial Holography, in proceedings of the 2022 Snowmass Summer Study, Seattle, WA, U.S.A., 7–26 July 2022, arXiv:2111.11392.
S. Caron-Huot, Z. Komargodski, A. Sever and A. Zhiboedov, Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude, JHEP 10 (2017) 026 [arXiv:1607.04253] [INSPIRE].
H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [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. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, The Duality Between Color and Kinematics and its Applications, arXiv:1909.01358.
J.J.M. Carrasco and I.A. Vazquez-Holm, Loop-Level Double-Copy for Massive Quantum Particles, Phys. Rev. D 103 (2021) 045002 [arXiv:2010.13435] [INSPIRE].
M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory. Volume 1, in Cambridge Monographs on Mathematical Physics, 25th anniversary edition, Cambridge University Press (2012) [https://doi.org/10.1017/CBO9781139248563] [INSPIRE].
J. Polchinski, String theory. Volume 1: An introduction to the bosonic string, in Cambridge Monographs on Mathematical Physics, Cambridge University Press (2007) [https://doi.org/10.1017/CBO9780511816079] [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].
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].
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].
Acknowledgments
We thank Md. Abhishek, Sourav Ballav, Chandan Jana and Amey Yeole for many useful discussions. We are grateful to Subramanya Hegde, Diksha Jain, Dileep Jatkar, Aakash Kumar, Alok Laddha, Manoj Mandal, especially Joydeep Chakravarty, Raj Patil and Sourav Ballav for their comment on the draft. MKNB is grateful to CSIR for the fellowship. AR is grateful to ICTP, Trieste, for hospitality during this work. AR would like to thank the organizers of the Regional Strings Meeting in NISER, Bhubaneswar where preliminay version of this work was presented. APS would like to thank HRI, Allahabad, for the hospitality during this work. We are grateful to the people of India for their generous funding for research in basic sciences.
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Balasubramanian, M.K.N., Chakraborty, K., Rudra, A. et al. On-shell supersymmetry and higher-spin amplitudes. J. High Energ. Phys. 2023, 37 (2023). https://doi.org/10.1007/JHEP06(2023)037
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DOI: https://doi.org/10.1007/JHEP06(2023)037