Abstract
Theories containing infinite number of higher spin fields require a particular definition of summation over spins consistent with their underlying symmetries. We consider a model of massless scalars interacting (via bilinear conserved currents) with conformal higher spin fields in flat space. We compute the tree-level four-scalar scattering amplitude using a natural prescription for summation over an infinite set of conformal higher spin exchanges and find that it vanishes. Independently, we show that the vanishing of the scalar scattering amplitude is, in fact, implied by the global conformal higher spin symmetry of this model. We also discuss one-loop corrections to the four-scalar scattering amplitude.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Beccaria and A.A. Tseytlin, On higher spin partition functions, J. Phys. A 48 (2015) 275401 [arXiv:1503.08143] [INSPIRE].
S. Giombi, I.R. Klebanov, S.S. Pufu, B.R. Safdi and G. Tarnopolsky, AdS description of induced higher-spin gauge theory, JHEP 10 (2013) 016 [arXiv:1306.5242] [INSPIRE].
S. Giombi and I.R. Klebanov, One loop tests of higher spin AdS/CFT, JHEP 12 (2013) 068 [arXiv:1308.2337] [INSPIRE].
A.A. Tseytlin, On partition function and Weyl anomaly of conformal higher spin fields, Nucl. Phys. B 877 (2013) 598 [arXiv:1309.0785] [INSPIRE].
S. Giombi, I.R. Klebanov and B.R. Safdi, Higher spin AdS d+1 /CFT d at one loop, Phys. Rev. D 89 (2014) 084004 [arXiv:1401.0825] [INSPIRE].
S. Giombi, I.R. Klebanov and A.A. Tseytlin, Partition functions and Casimir energies in higher spin AdS d+1 /CFT d , Phys. Rev. D 90 (2014) 024048 [arXiv:1402.5396] [INSPIRE].
M. Beccaria, X. Bekaert and A.A. Tseytlin, Partition function of free conformal higher spin theory, JHEP 08 (2014) 113 [arXiv:1406.3542] [INSPIRE].
M. Beccaria and A.A. Tseytlin, Higher spins in AdS 5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT, JHEP 11 (2014) 114 [arXiv:1410.3273] [INSPIRE].
X. Bekaert, E. Joung and J. Mourad, On higher spin interactions with matter, JHEP 05 (2009) 126 [arXiv:0903.3338] [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.
C. Aragone and S. Deser, Consistency problems of hypergravity, Phys. Lett. B 86 (1979) 161 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, On the gravitational interaction of massless higher spin fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Conformal supergravity, Phys. Rept. 119 (1985) 233 [INSPIRE].
E.S. Fradkin and V.Ya. Linetsky, Cubic interaction in conformal theory of integer higher spin fields in four-dimensional space-time, Phys. Lett. B 231 (1989) 97 [INSPIRE].
A.A. Tseytlin, On limits of superstring in AdS 5 × S 5, Theor. Math. Phys. 133 (2002) 1376 [hep-th/0201112] [INSPIRE].
A.Y. Segal, Conformal higher spin theory, Nucl. Phys. B 664 (2003) 59 [hep-th/0207212] [INSPIRE].
X. Bekaert, E. Joung and J. Mourad, Effective action in a higher-spin background, JHEP 02 (2011) 048 [arXiv:1012.2103] [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
N.S. Craigie, V.K. Dobrev and I.T. Todorov, Conformally covariant composite operators in quantum chromodynamics, Annals Phys. 159 (1985) 411 [INSPIRE].
M.A. Vasiliev, Closed equations for interacting gauge fields of all spins, JETP Lett. 51 (1990) 503 [INSPIRE].
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories in various dimensions, Fortsch. Phys. 52 (2004) 702 [hep-th/0401177] [INSPIRE].
L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [INSPIRE].
M.A. Vasiliev, Conformal higher spin symmetries of 4D massless supermultiplets and OSp(L, 2M) invariant equations in generalized (super)space, Phys. Rev. D 66 (2002) 066006 [hep-th/0106149] [INSPIRE].
M.A. Vasiliev, On conformal, \( \mathrm{S}\mathrm{L}\left(4,\mathrm{\mathbb{R}}\right) \) and Sp(8, R) symmetries of 4D massless fields, Nucl. Phys. B 793 (2008) 469 [arXiv:0707.1085] [INSPIRE].
O.V. Shaynkman, Bosonic Fradkin-Tseytlin equations unfolded, arXiv:1412.7743 [INSPIRE].
T. Nutma and M. Taronna, On conformal higher spin wave operators, JHEP 06 (2014) 066 [arXiv:1404.7452] [INSPIRE].
E. Joung and K. Mkrtchyan, Notes on higher-spin algebras: minimal representations and structure constants, JHEP 05 (2014) 103 [arXiv:1401.7977] [INSPIRE].
R.R. Metsaev, BRST invariant effective action of shadow fields, conformal fields and AdS/CFT, Theor. Math. Phys. 181 (2014) 1548 [arXiv:1407.2601] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1512.08896
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Joung, E., Nakach, S. & Tseytlin, A.A. Scalar scattering via conformal higher spin exchange. J. High Energ. Phys. 2016, 125 (2016). https://doi.org/10.1007/JHEP02(2016)125
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2016)125