Abstract
We give explicit construction for massive higher spin supermultiplets for the case of minimal supersymmetry in d = 3 and find the corresponding Lagrangian formulations. We show that all such massive supermultiplets can be straightforwardly constructed out of the appropriately chosen set of massless ones exactly in the same way as the gauge invariant description for the massive bosonic (fermionic) field with spin s can be obtained using a set of massless fields with spins s, s − 1, . . . , 0(1/2). Moreover, such construction for the massive supermultiplets turns out to be perfectly consistent with our previous results on the gauge invariant Lagrangian formulation for massive higher spin bosons and fermions in d = 3.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.A. Vasiliev, Higher spin gauge theories in various dimensions, Fortsch. Phys. 52 (2004) 702 [hep-th/0401177] [INSPIRE].
D. Sorokin, Introduction to the classical theory of higher spins, AIP Conf. Proc. 767 (2005) 172 [hep-th/0405069] [INSPIRE].
X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [INSPIRE].
A. Fotopoulos and M. Tsulaia, Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation, Int. J. Mod. Phys. A 24 (2009) 1 [arXiv:0805.1346] [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. Sagnotti, Notes on Strings and Higher Spins, J. Phys. A 46 (2013) 214006 [arXiv:1112.4285] [INSPIRE].
V.E. Didenko and E.D. Skvortsov, Elements of Vasiliev theory, arXiv:1401.2975 [INSPIRE].
M.A. Vasiliev, Higher-Spin Theory and Space-Time Metamorphoses, Lect. Notes Phys. 892 (2015) 227 [arXiv:1404.1948] [INSPIRE].
S. Deser and R. Jackiw, Statistics without spin: massless D = 3 systems, Phys. Lett. B 263 (1991) 431 [INSPIRE].
T. Curtright, Massless Field Supermultiplets with Arbitrary Spin, Phys. Lett. B 85 (1979) 214 [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].
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., S.M. Kuzenko and A.G. Sibiryakov, Towards a unified theory of massless superfields of all superspins, Phys. Lett. B 394 (1997) 343 [hep-th/9611193] [INSPIRE].
S.J. Gates Jr., S.M. Kuzenko and A.G. Sibiryakov, N = 2 supersymmetry of higher superspin massless theories, Phys. Lett. B 412 (1997) 59 [hep-th/9609141] [INSPIRE].
I.L. Buchbinder, S.J. Gates Jr., W.D. Linch III and J. Phillips, New 4D, N = 1 superfield theory: Model of free massive superspin- \( \frac{3}{2} \) 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].
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. and S.M. Kuzenko, 4D, N = 1 higher spin gauge superfields and quantized twistors, JHEP 10 (2005) 008 [hep-th/0506255] [INSPIRE].
S.J. Gates Jr., S.M. Kuzenko and G. Tartaglino-Mazzucchelli, New massive supergravity multiplets, JHEP 02 (2007) 052 [hep-th/0610333] [INSPIRE].
S.J. Gates Jr. and K. Koutrolikos, A dynamical theory for linearized massive superspin 3/2, JHEP 03 (2014) 030 [arXiv:1310.7387] [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Three-dimensional N = 2 (AdS) supergravity and associated supercurrents, JHEP 12 (2011) 052 [arXiv:1109.0496] [INSPIRE].
S.M. Kuzenko, U. Lindström, M. Roček, I. Sachs and G. Tartaglino-Mazzucchelli, Three-dimensional \( \mathcal{N}=2 \) supergravity theories: From superspace to components, Phys. Rev. D 89 (2014) 085028 [arXiv:1312.4267] [INSPIRE].
S.M. Kuzenko and J. Novak, Supergravity-matter actions in three dimensions and Chern-Simons terms, JHEP 05 (2014) 093 [arXiv:1401.2307] [INSPIRE].
Yu.M. Zinoviev, Massive spin two supermultiplets, hep-th/0206209 [INSPIRE].
Yu.M. Zinoviev, Massive supermultiplets with spin 3/2, JHEP 05 (2007) 092 [hep-th/0703118] [INSPIRE].
Yu.M. Zinoviev, Massive N = 1 supermultiplets with arbitrary superspins, Nucl. Phys. B 785 (2007) 98 [arXiv:0704.1535] [INSPIRE].
Yu.M. Zinoviev, On massive high spin particles in AdS, hep-th/0108192 [INSPIRE].
R.R. Metsaev, Gauge invariant formulation of massive totally symmetric fermionic fields in (A)dS space, Phys. Lett. B 643 (2006) 205 [hep-th/0609029] [INSPIRE].
I.L. Buchbinder, T.V. Snegirev and Yu.M. Zinoviev, Gauge invariant Lagrangian formulation of massive higher spin fields in (A)dS 3 space, Phys. Lett. B 716 (2012) 243 [arXiv:1207.1215] [INSPIRE].
I.L. Buchbinder, T.V. Snegirev and Yu.M. Zinoviev, Frame-like gauge invariant Lagrangian formulation of massive fermionic higher spin fields in AdS 3 space, Phys. Lett. B 738 (2014) 258 [arXiv:1407.3918] [INSPIRE].
I.V. Tyutin and M.A. Vasiliev, Lagrangian formulation of irreducible massive fields of arbitrary spin in (2 + 1)-dimensions, Teor. Mat. Fiz. 113N1 (1997) 45 [Theor. Math. Phys. 113 (1997) 1244] [hep-th/9704132] [INSPIRE].
E.A. Bergshoeff, M. Kovačević, L. Parra, J. Rosseel, Y. Yin and T. Zojer, New Massive Supergravity and Auxiliary Fields, Class. Quant. Grav. 30 (2013) 195004 [arXiv:1304.5445] [INSPIRE].
S.M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, Higher derivative couplings and massive supergravity in three dimensions, JHEP 09 (2015) 081 [arXiv:1506.09063] [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: 1508.02829
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
Buchbinder, I., Snegirev, T. & Zinoviev, Y. Lagrangian formulation of the massive higher spin supermultiplets in three dimensional space-time. J. High Energ. Phys. 2015, 148 (2015). https://doi.org/10.1007/JHEP10(2015)148
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2015)148