Abstract
An explicit form for the Lagrangian of a massive arbitrary half-integer super-spin Y = s + 1/2 supermultiplet is obtained in 4D, \( \mathcal{N} \) = 1 superspace. This is accomplished by the introduction of a tower of pairs of auxiliary superfields of increasing rank which are required to vanish on-shell for free theories. In the massless limit almost all auxiliary super- fields decouple except one, which plays the role of compensator as required by the emergent gauge redundancy of the Lagrangian description of the massless theory. The number of off-shell degrees of freedom carried by the theory is \( \frac{8}{3} \) (s + 1)(4s2 + 11s + 3). For s = 1 our results are in agreement with those obtained in [1].
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S.J. Gates Jr. and K. Koutrolikos, A dynamical theory for linearized massive superspin 3/2, JHEP 03 (2014) 030 [arXiv:1310.7387] [INSPIRE].
G.L. Kane and M. Shifman eds., The supersymmetric world: The beginning of the theory, World Scientific (2000) [INSPIRE].
M.A. Shifman ed., The many faces of the superworld: Yuri Golfand memorial volume, Singapore (2000) [INSPIRE].
T. Curtright, Massless Field Supermultiplets With Arbitrary Spin, Phys. Lett. B 85 (1979) 219 [INSPIRE].
M.A. Vasiliev, ‘Gauge’ form of description of massless fields with arbitrary spin (in Russian), Yad. Fiz. 32 (1980) 855 [INSPIRE].
S.M. Kuzenko, A.G. Sibiryakov and V.V. Postnikov, Massless gauge superfields of higher half integer superspins, JETP Lett. 57 (1993) 534 [INSPIRE].
S.M. Kuzenko and A.G. Sibiryakov, Massless gauge superfields of higher integer superspins, JETP Lett. 57 (1993) 539 [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 [arXiv:1112.4612] [INSPIRE].
S.J. Gates Jr. and K. Koutrolikos, On 4D, \( \mathcal{N} \) = 1 massless gauge superfields of arbitrary superhelicity, JHEP 06 (2014) 098 [arXiv:1310.7385] [INSPIRE].
S.J. Gates Jr. and K. Koutrolikos, On 4D, \( \mathcal{N} \) = 1 Massless Gauge Superfields of Higher Superspin: Half-Odd-Integer Case, arXiv:1310.7386 [INSPIRE].
I.L. Buchbinder, S.J. Gates and K. Koutrolikos, Hierarchy of Supersymmetric Higher Spin Connections, Phys. Rev. D 102 (2020) 125018 [arXiv:2010.02061] [INSPIRE].
I.L. Buchbinder, S.J. Gates and K. Koutrolikos, Higher Spin Superfield interactions with the Chiral Supermultiplet: Conserved Supercurrents and Cubic Vertices, Universe 4 (2018) 6 [arXiv:1708.06262] [INSPIRE].
J. Hutomo and S.M. Kuzenko, Non-conformal higher spin supercurrents, Phys. Lett. B 778 (2018) 242 [arXiv:1710.10837] [INSPIRE].
K. Koutrolikos, P. Kočí and R. von Unge, Higher Spin Superfield interactions with Complex linear Supermultiplet: Conserved Supercurrents and Cubic Vertices, JHEP 03 (2018) 119 [arXiv:1712.05150] [INSPIRE].
I.L. Buchbinder, S.J. Gates and K. Koutrolikos, Interaction of supersymmetric nonlinear sigma models with external higher spin superfields via higher spin supercurrents, JHEP 05 (2018) 204 [arXiv:1804.08539] [INSPIRE].
I.L. Buchbinder, S.J. Gates and K. Koutrolikos, Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions, JHEP 08 (2018) 055 [arXiv:1805.04413] [INSPIRE].
E.I. Buchbinder, J. Hutomo and S.M. Kuzenko, Higher spin supercurrents in anti-de Sitter space, JHEP 09 (2018) 027 [arXiv:1805.08055] [INSPIRE].
I.L. Buchbinder, S.J. Gates and K. Koutrolikos, Integer superspin supercurrents of matter supermultiplets, JHEP 05 (2019) 031 [arXiv:1811.12858] [INSPIRE].
S.J. Gates and K. Koutrolikos, Progress on cubic interactions of arbitrary superspin supermultiplets via gauge invariant supercurrents, Phys. Lett. B 797 (2019) 134868 [arXiv:1904.13336] [INSPIRE].
R.R. Metsaev, Cubic interaction vertices for N = 1 arbitrary spin massless supermultiplets in flat space, JHEP 08 (2019) 130 [arXiv:1905.11357] [INSPIRE].
R.R. Metsaev, Cubic interactions for arbitrary spin \( \mathcal{N} \)-extended massless supermultiplets in 4d flat space, JHEP 11 (2019) 084 [arXiv:1909.05241] [INSPIRE].
M.V. Khabarov and Y.M. Zinoviev, Cubic interaction vertices for massless higher spin supermultiplets in d = 4, JHEP 02 (2021) 167 [arXiv:2012.00482] [INSPIRE].
L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. 1. The boson case, Phys. Rev. D 9 (1974) 898 [INSPIRE].
L.P.S. Singh and C.R. Hagen, Lagrangian formulation for arbitrary spin. 2. The fermion case, Phys. Rev. D 9 (1974) 910 [INSPIRE].
P.A. Dirac, Relativistic wave equations, Proc. Roy. Soc. Lond. A 155 (1936) 447.
Y.M. Zinoviev, Massive N = 1 supermultiplets with arbitrary superspins, Nucl. Phys. B 785 (2007) 98 [arXiv:0704.1535] [INSPIRE].
I.L. Buchbinder, M.V. Khabarov, T.V. Snegirev and Y.M. Zinoviev, Lagrangian formulation of the massive higher spin N = 1 supermultiplets in AdS4 space, Nucl. Phys. B 942 (2019) 1 [arXiv:1901.09637] [INSPIRE].
M.V. Khabarov and Y.M. Zinoviev, Massive higher spin fields in the frame-like multispinor formalism, Nucl. Phys. B 948 (2019) 114773 [arXiv:1906.03438] [INSPIRE].
Y.M. Zinoviev, Massive Higher Spins in Multispinor Formalism, Phys. Part. Nucl. Lett. 17 (2020) 692 [INSPIRE].
M.V. Khabarov and Y.M. Zinoviev, Massive higher spin supermultiplets unfolded, Nucl. Phys. B 953 (2020) 114959 [arXiv:2001.07903] [INSPIRE].
I.L. Buchbinder, S.J. Gates Jr., W.D. Linch, III and J. Phillips, New 4-D, N = 1 superfield theory: Model of free massive superspin 3/2 multiplet, Phys. Lett. B 535 (2002) 280 [hep-th/0201096] [INSPIRE].
I.L. Buchbinder, S.J. Gates Jr., W.D. Linch, III and J. Phillips, Dynamical superfield theory of free massive superspin-1 multiplet, Phys. Lett. B 549 (2002) 229 [hep-th/0207243] [INSPIRE].
T. Gregoire, M.D. Schwartz and Y. Shadmi, Massive supergravity and deconstruction, JHEP 07 (2004) 029 [hep-th/0403224] [INSPIRE].
I.L. Buchbinder, S. James Gates Jr., S.M. Kuzenko and J. Phillips, Massive 4D, N = 1 superspin 1 & 3/2 multiplets and dualities, JHEP 02 (2005) 056 [hep-th/0501199] [INSPIRE].
S.J. Gates Jr., S.M. Kuzenko and G. Tartaglino-Mazzucchelli, New massive supergravity multiplets, JHEP 02 (2007) 052 [hep-th/0610333] [INSPIRE].
I. Bars, Supergroups and Their Representations, Lectures Appl. Math. 21 (1983) 17 [INSPIRE].
S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace Or One Thousand and One Lessons in Supersymmetry, Frontiers in Physics 58 (1983) [hep-th/0108200] [INSPIRE].
P. Srivastava, Supersymmetry, superfields and supergravity: an introduction, Bristol, U.K. (1986).
I. Buchbinder and S. Kuzenko, Ideas and methods of supersymmetry and supergravity: A Walk through superspace, Bristol, U.K. (1995).
K. Koutrolikos, On Lagrangian Formulation of Higher-Superspin Irreducible Representations of the Super-Poincaré Group, Ph.D. Thesis, Maryland University, Maryland, U.S.A. (2013).
I.L. Buchbinder, S.J. Gates and K. Koutrolikos, Superfield continuous spin equations of motion, Phys. Lett. B 793 (2019) 445 [arXiv:1903.08631] [INSPIRE].
S.J. Gates and K. Koutrolikos, From Diophantus to Supergravity and massless higher spin multiplets, JHEP 11 (2017) 063 [arXiv:1707.00194] [INSPIRE].
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Dedicated to S. James Gates Jr. on the occasion of his 70th birthday
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Koutrolikos, K. Superspace formulation of massive half-integer superspin. J. High Energ. Phys. 2021, 254 (2021). https://doi.org/10.1007/JHEP03(2021)254
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DOI: https://doi.org/10.1007/JHEP03(2021)254