Abstract
We propose a new off-shell formulation for the massless \( \mathcal{N} \) = 1 supersymmetric multiplet of integer superspin s in four dimensions, where s = 2, 3, . . . (the s = 1 case corresponds to the gravitino multiplet). Its gauge freedom matches that of the superconformal superspin-s multiplet described in arXiv:1701.00682. The gauge-invariant action involves two compensating multiplets in addition to the superconformal superspin-s multiplet. Upon imposing a partial gauge fixing, this action reduces to the one describing the so-called longitudinal formulation for the massless superspin-s multiplet. Our new model is shown to possess a dual realisation obtained by applying a superfield Legendre transformation. We present a non-conformal higher spin supercurrent multiplet associated with the new integer superspin theory. This fermionic supercurrent is shown to occur in the Fayet-Sohnius model for a massive \( \mathcal{N} \) = 2 hypermultiplet. We also give a new off-shell realisation for the massless gravitino multiplet.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Curtright, Massless Field Supermultiplets With Arbitrary Spin, Phys. Lett. B 85 (1979) 219 [INSPIRE].
C. Fronsdal, Massless Fields with Integer Spin, Phys. Rev. D 18 (1978) 3624 [INSPIRE].
J. Fang and C. Fronsdal, Massless Fields with Half Integral Spin, Phys. Rev. D 18 (1978) 3630 [INSPIRE].
M.A. Vasiliev, “Gauge” form of description of massless fields with arbitrary spin (in Russian), Yad. Fiz. 32 (1980) 855 [Sov. J. Nucl. Phys. 32 (1980) 439] [INSPIRE].
S. Ferrara and B. Zumino, Transformation Properties of the Supercurrent, Nucl. Phys. B 87 (1975) 207 [INSPIRE].
M.P. Bellon and S. Ouvry, D = 4 Supersymmetry for Gauge Fields of Any Spin, Phys. Lett. B 187 (1987) 93 [INSPIRE].
M.P. Bellon and S. Ouvry, D = 4 Superspace Formulation for Higher Spin Fields, Phys. Lett. B 193 (1987) 67 [INSPIRE].
S.M. Kuzenko and A.G. Sibiryakov, Free massless higher superspin superfields on the anti-de Sitter superspace, Phys. Atom. Nucl. 57 (1994) 1257 [Yad. Fiz. 57 (1994) 1326] [arXiv:1112.4612] [INSPIRE].
S.M. Kuzenko, A.G. Sibiryakov and V.V. Postnikov, Massless gauge superfields of higher half integer superspins, JETP Lett. 57 (1993) 534 [Pisma Zh. Eksp. Teor. Fiz. 57 (1993) 521] [INSPIRE].
S.M. Kuzenko and A.G. Sibiryakov, Massless gauge superfields of higher integer superspins, JETP Lett. 57 (1993) 539 [Pisma Zh. Eksp. Teor. Fiz. 57 (1993) 526] [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity, Or a Walk Through Superspace, revised edition, IOP Publishing, Bristol U.K. (1998).
E.S. Fradkin and A.A. Tseytlin, Conformal supergravity, Phys. Rept. 119 (1985) 233 [INSPIRE].
E.S. Fradkin and V.Y. Linetsky, Superconformal Higher Spin Theory in the Cubic Approximation, Nucl. Phys. B 350 (1991) 274 [INSPIRE].
S.M. Kuzenko, R. Manvelyan and S. Theisen, Off-shell superconformal higher spin multiplets in four dimensions, JHEP 07 (2017) 034 [arXiv:1701.00682] [INSPIRE].
S. Ferrara and B. Zumino, Structure of Conformal Supergravity, Nucl. Phys. B 134 (1978) 301 [INSPIRE].
S.J. Gates Jr., M.T. Grisaru, M. Roček and W. Siegel, Superspace Or One Thousand and One Lessons in Supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
U. Lindström and M. Roček, New hyperkähler metrics and new supermultiplets, Commun. Math. Phys. 115 (1988) 21 [INSPIRE].
S.J. Gates Jr. and S.M. Kuzenko, 4-D, N = 2 supersymmetric off-shell σ-models on the cotangent bundles of Kähler manifolds, Fortsch. Phys. 48 (2000) 115 [hep-th/9903013] [INSPIRE].
P. Fayet, Fermi-Bose Hypersymmetry, Nucl. Phys. B 113 (1976) 135 [INSPIRE].
M.F. Sohnius, Supersymmetry and Central Charges, Nucl. Phys. B 138 (1978) 109 [INSPIRE].
J. Hutomo and S.M. Kuzenko, Non-conformal higher spin supercurrents, Phys. Lett. B 778 (2018) 242 [arXiv:1710.10837] [INSPIRE].
P.S. Howe, K.S. Stelle and P.K. Townsend, Supercurrents, Nucl. Phys. B 192 (1981) 332 [INSPIRE].
I.L. Buchbinder, S.J. Gates Jr. and K. Koutrolikos, Higher Spin Superfield interactions with the Chiral Supermultiplet: Conserved Supercurrents and Cubic Vertices, Universe 4 (2018) 6 [arXiv:1708.06262] [INSPIRE].
S.M. Kuzenko and S. Theisen, Correlation functions of conserved currents in N = 2 superconformal theory, Class. Quant. Grav. 17 (2000) 665 [hep-th/9907107] [INSPIRE].
S.J. Gates Jr. and W. Siegel, (32, 1) Superfield of O(2) Supergravity, Nucl. Phys. B 164 (1980) 484 [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, Minimal set of auxiliary fields and S-matrix for extended supergravity, Lett. Nuovo Cim. 25 (1979) 79 [INSPIRE].
B. de Wit and J.W. van Holten, Multiplets of Linearized SO(2) Supergravity, Nucl. Phys. B 155 (1979) 530 [INSPIRE].
U. Lindström and M. Roček, Scalar Tensor Duality and N = 1, N = 2 Nonlinear σ-models, Nucl. Phys. B 222 (1983) 285 [INSPIRE].
D. Butter and S.M. Kuzenko, N = 2 supergravity and supercurrents, JHEP 12 (2010) 080 [arXiv:1011.0339] [INSPIRE].
V.I. Ogievetsky and E. Sokatchev, On Gauge Spinor Superfield, JETP Lett. 23 (1976) 58 [INSPIRE].
V.I. Ogievetsky and E. Sokatchev, Superfield Equations of Motion, J. Phys. A 10 (1977) 2021 [INSPIRE].
B. de Wit, R. Philippe and A. Van Proeyen, The Improved Tensor Multiplet in N = 2 Supergravity, Nucl. Phys. B 219 (1983) 143 [INSPIRE].
S.M. Kuzenko, U. Lindström, M. Roček and G. Tartaglino-Mazzucchelli, 4D N = 2 Supergravity and Projective Superspace, JHEP 09 (2008) 051 [arXiv:0805.4683] [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: 1711.11364
Dedicated to Professor Ulf Lindström on the occasion of his 70th birthday
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
Hutomo, J., Kuzenko, S.M. The massless integer superspin multiplets revisited. J. High Energ. Phys. 2018, 137 (2018). https://doi.org/10.1007/JHEP02(2018)137
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2018)137