Abstract
Massive arbitrary spin supermultiplets and massless (scalar and spin one-half) supermultiplets of the N = 2 Poincaré superalgebra in three-dimensional flat space are considered. Both the integer spin and half-integer spin supermultiplets are studied. For such massive and massless supermultiplets, a formulation in terms of light-cone gauge unconstrained superfields defined in a momentum superspace is developed. For the supermultiplets under consideration a superspace first derivative representation for all cubic interaction vertices is obtained. A superspace representation for dynamical generators of the N = 2 Poincaré superalgebra is also found.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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 [hep-th/9704132] [INSPIRE].
S. F. Prokushkin and M. A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3-D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [INSPIRE].
S. F. Prokushkin, A. Y. Segal and M. A. Vasiliev, Coordinate free action for AdS3 higher spin matter systems, Phys. Lett. B 478 (2000) 333 [hep-th/9912280] [INSPIRE].
R. Bonezzi, N. Boulanger, E. Sezgin and P. Sundell, An Action for Matter Coupled Higher Spin Gravity in Three Dimensions, JHEP 05 (2016) 003 [arXiv:1512.02209] [INSPIRE].
I. L. Buchbinder, T. V. Snegirev and Y. M. Zinoviev, On gravitational interactions for massive higher spins in AdS3, J. Phys. A 46 (2013) 214015 [arXiv:1208.0183] [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Towards metric-like higher-spin gauge theories in three dimensions, J. Phys. A 46 (2013) 214017 [arXiv:1208.1851] [INSPIRE].
A. Campoleoni and M. Henneaux, Asymptotic symmetries of three-dimensional higher-spin gravity: the metric approach, JHEP 03 (2015) 143 [arXiv:1412.6774] [INSPIRE].
K. Mkrtchyan, Cubic interactions of massless bosonic fields in three dimensions, Phys. Rev. Lett. 120 (2018) 221601 [arXiv:1712.10003] [INSPIRE].
P. Kessel and K. Mkrtchyan, Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices, Phys. Rev. D 97 (2018) 106021 [arXiv:1803.02737] [INSPIRE].
S. Fredenhagen, O. Krüger and K. Mkrtchyan, Vertex-Constraints in 3D Higher Spin Theories, Phys. Rev. Lett. 123 (2019) 131601 [arXiv:1905.00093] [INSPIRE].
S. M. Kuzenko and M. Ponds, Higher-spin Cotton tensors and massive gauge-invariant actions in AdS3, JHEP 05 (2021) 275 [arXiv:2103.11673] [INSPIRE].
R. R. Metsaev, Cubic interactions of arbitrary spin fields in 3d flat space, J. Phys. A 53 (2020) 445401 [arXiv:2005.12224] [INSPIRE].
M. B. Green and J. H. Schwarz, Extended Supergravity in Ten-Dimensions, Phys. Lett. B 122 (1983) 143 [INSPIRE].
M. B. Green, J. H. Schwarz and L. Brink, Superfield Theory of Type II Superstrings, Nucl. Phys. B 219 (1983) 437 [INSPIRE].
R. R. Metsaev, Eleven dimensional supergravity in light cone gauge, Phys. Rev. D 71 (2005) 085017 [hep-th/0410239] [INSPIRE].
R. R. Metsaev and A. A. Tseytlin, Superparticle and superstring in AdS3 × S3 Ramond-Ramond background in light cone gauge, J. Math. Phys. 42 (2001) 2987 [hep-th/0011191] [INSPIRE].
T. Klose and T. McLoughlin, A light-cone approach to three-point functions in AdS5 × S5, JHEP 04 (2012) 080 [arXiv:1106.0495] [INSPIRE].
L. Mezincescu and P. K. Townsend, Quantum 3D Superstrings, Phys. Rev. D 84 (2011) 106006 [arXiv:1106.1374] [INSPIRE].
P. A. M. Dirac, Forms of Relativistic Dynamics, Rev. Mod. Phys. 21 (1949) 392 [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].
A. K. H. Bengtsson, I. Bengtsson and L. Brink, Cubic Interaction Terms for Arbitrarily Extended Supermultiplets, Nucl. Phys. B 227 (1983) 41 [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].
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].
M. V. Khabarov and Y. M. Zinoviev, Massless higher spin cubic vertices in flat four dimensional space, JHEP 08 (2020) 112 [arXiv:2005.09851] [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].
K. Krasnov, E. Skvortsov and T. Tran, Actions for Self-dual Higher Spin Gravities, JHEP 08 (2021) 076 [arXiv:2105.12782] [INSPIRE].
K. Krasnov and E. Skvortsov, Flat Self-dual Gravity, JHEP 08 (2021) 082 [arXiv:2106.01397] [INSPIRE].
T. Tran, Twistor constructions for higher-spin extensions of (self-dual) Yang-Mills, JHEP 11 (2021) 117 [arXiv:2107.04500] [INSPIRE].
S. M. Kuzenko and G. Tartaglino-Mazzucchelli, Supertwistor realisations of AdS superspaces, arXiv:2108.03907 [INSPIRE].
D. V. Uvarov, Oscillator approach to quantization of AdS5 × S5 superparticle in twistor formulation, Phys. Lett. B 815 (2021) 136132 [arXiv:2004.03356] [INSPIRE].
D. V. Uvarov, Supertwistor formulation for massless superparticle in AdS5 × S5 superspace, Nucl. Phys. B 936 (2018) 690 [arXiv:1807.08318] [INSPIRE].
R. R. Metsaev, Massive fields in AdS3 and compactification in AdS space time, Nucl. Phys. B Proc. Suppl. 102 (2001) 100 [hep-th/0103088] [INSPIRE].
R. R. Metsaev, Light-cone gauge cubic interaction vertices for massless fields in AdS4, Nucl. Phys. B 936 (2018) 320 [arXiv:1807.07542] [INSPIRE].
E. Skvortsov, Light-Front Bootstrap for Chern-Simons Matter Theories, JHEP 06 (2019) 058 [arXiv:1811.12333] [INSPIRE].
Y. M. Zinoviev, On higher spin cubic interactions in d = 3, JHEP 11 (2021) 022 [arXiv:2109.08480] [INSPIRE].
S. M. Kuzenko and D. X. Ogburn, Off-shell higher spin N = 2 supermultiplets in three dimensions, Phys. Rev. D 94 (2016) 106010 [arXiv:1603.04668] [INSPIRE].
S. M. Kuzenko and M. Tsulaia, Off-shell massive N = 1 supermultiplets in three dimensions, Nucl. Phys. B 914 (2017) 160 [arXiv:1609.06910] [INSPIRE].
I. L. Buchbinder, T. V. Snegirev and Y. M. Zinoviev, Lagrangian description of massive higher spin supermultiplets in AdS3 space, JHEP 08 (2017) 021 [arXiv:1705.06163] [INSPIRE].
I. L. Buchbinder, T. V. Snegirev and Y. M. Zinoviev, Supersymmetric higher spin models in three dimensional spaces, Symmetry 10 (2017) 9 [arXiv:1711.11450] [INSPIRE].
S. M. Kuzenko and M. Ponds, Topologically massive higher spin gauge theories, JHEP 10 (2018) 160 [arXiv:1806.06643] [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].
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].
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].
K. Koutrolikos, Superspace formulation of massive half-integer superspin, JHEP 03 (2021) 254 [arXiv:2012.12225] [INSPIRE].
I. Buchbinder, E. Ivanov and N. Zaigraev, Unconstrained off-shell superfield formulation of 4D, \( \mathcal{N} \) = 2 supersymmetric higher spins, arXiv:2109.07639 [INSPIRE].
L. Bonora and S. Giaccari, Supersymmetric HS Yang-Mills-like models, Universe 6 (2020) 245 [arXiv:2011.00734] [INSPIRE].
R. R. Metsaev, Cubic interaction vertices of massive and massless higher spin fields, Nucl. Phys. B 759 (2006) 147 [hep-th/0512342] [INSPIRE].
R. R. Metsaev, Cubic interaction vertices for fermionic and bosonic arbitrary spin fields, Nucl. Phys. B 859 (2012) 13 [arXiv:0712.3526] [INSPIRE].
R. Manvelyan, K. Mkrtchyan and W. Rühl, General trilinear interaction for arbitrary even higher spin gauge fields, Nucl. Phys. B 836 (2010) 204 [arXiv:1003.2877] [INSPIRE].
A. Sagnotti and M. Taronna, String Lessons for Higher-Spin Interactions, Nucl. Phys. B 842 (2011) 299 [arXiv:1006.5242] [INSPIRE].
R. Manvelyan, K. Mkrtchyan and W. Ruehl, A Generating function for the cubic interactions of higher spin fields, Phys. Lett. B 696 (2011) 410 [arXiv:1009.1054] [INSPIRE].
E. Joung and M. Taronna, Cubic interactions of massless higher spins in (A)dS: metric-like approach, Nucl. Phys. B 861 (2012) 145 [arXiv:1110.5918] [INSPIRE].
N. Boulanger, D. Ponomarev and E. D. Skvortsov, Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space, JHEP 05 (2013) 008 [arXiv:1211.6979] [INSPIRE].
X. Bekaert, N. Boulanger and S. Cnockaert, Spin three gauge theory revisited, JHEP 01 (2006) 052 [hep-th/0508048] [INSPIRE].
A. Fotopoulos and M. Tsulaia, On the Tensionless Limit of String theory, Off-Shell Higher Spin Interaction Vertices and BCFW Recursion Relations, JHEP 11 (2010) 086 [arXiv:1009.0727] [INSPIRE].
R. R. Metsaev, BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields, Phys. Lett. B 720 (2013) 237 [arXiv:1205.3131] [INSPIRE].
I. L. Buchbinder and A. A. Reshetnyak, General cubic interacting vertex for massless integer higher spin fields, Phys. Lett. B 820 (2021) 136470 [arXiv:2105.12030] [INSPIRE].
K. B. Alkalaev and M. A. Vasiliev, N = 1 supersymmetric theory of higher spin gauge fields in AdS5 at the cubic level, Nucl. Phys. B 655 (2003) 57 [hep-th/0206068] [INSPIRE].
K. Alkalaev, FV-type action for AdS5 mixed-symmetry fields, JHEP 03 (2011) 031 [arXiv:1011.6109] [INSPIRE].
R. Rahman, The Uniqueness of Hypergravity, JHEP 11 (2019) 115 [arXiv:1905.04109] [INSPIRE].
B. E. W. Nilsson, On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field, JHEP 08 (2016) 142 [arXiv:1506.03328] [INSPIRE].
T. Basile, R. Bonezzi and N. Boulanger, The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields, JHEP 04 (2017) 054 [arXiv:1701.08645] [INSPIRE].
S. M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, N = 6 superconformal gravity in three dimensions from superspace, JHEP 01 (2014) 121 [arXiv:1308.5552] [INSPIRE].
M. Henneaux, V. Lekeu, A. Leonard, J. Matulich and S. Prohazka, Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields, JHEP 11 (2018) 156 [arXiv:1810.04457] [INSPIRE].
E. I. Buchbinder, D. Hutchings, J. Hutomo and S. M. Kuzenko, Linearised actions for \( \mathcal{N} \)-extended (higher-spin) superconformal gravity, JHEP 08 (2019) 077 [arXiv:1905.12476] [INSPIRE].
M. Grigoriev, I. Lovrekovic and E. Skvortsov, New Conformal Higher Spin Gravities in 3d, JHEP 01 (2020) 059 [arXiv:1909.13305] [INSPIRE].
D. Ponomarev, 3d conformal fields with manifest sl(2, ℂ), JHEP 06 (2021) 055 [arXiv:2104.02770] [INSPIRE].
R. R. Metsaev, Ordinary-derivative formulation of conformal totally symmetric arbitrary spin bosonic fields, JHEP 06 (2012) 062 [arXiv:0709.4392] [INSPIRE].
R. R. Metsaev, Long, partial-short, and special conformal fields, JHEP 05 (2016) 096 [arXiv:1604.02091] [INSPIRE].
R. R. Metsaev, Interacting light-cone gauge conformal fields, arXiv:1612.06348 [INSPIRE].
D. Ponomarev and E. D. Skvortsov, Light-Front Higher-Spin Theories in Flat Space, J. Phys. A 50 (2017) 095401 [arXiv:1609.04655] [INSPIRE].
E. Skvortsov, T. Tran and M. Tsulaia, A Stringy theory in three dimensions and Massive Higher Spins, Phys. Rev. D 102 (2020) 126010 [arXiv:2006.05809] [INSPIRE].
R. R. Metsaev, Poincaré invariant dynamics of massless higher spins: Fourth order analysis on mass shell, Mod. Phys. Lett. A 6 (1991) 359 [INSPIRE].
R. R. Metsaev, S matrix approach to massless higher spins theory. 2: The Case of internal symmetry, Mod. Phys. Lett. A 6 (1991) 2411 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2110.02696
Rights and permissions
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.
About this article
Cite this article
Metsaev, R.R. Superfield approach to interacting N = 2 massive and massless supermultiplets in 3d flat space. J. High Energ. Phys. 2021, 69 (2021). https://doi.org/10.1007/JHEP12(2021)069
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2021)069