Abstract
We elaborate on the structure of higher-spin \( \mathcal{N} \) = 2 supercurrent multiplets in four dimensions. It is shown that associated with every conformal supercurrent \( {J}_{\alpha (m)\overset{\cdot }{\alpha }(n)} \) (with m, n non-negative integers) is a descendant \( {J}_{\alpha \left(m+1\right)\overset{\cdot }{\alpha}\left(n+1\right)}^{ij} \) with the following properties: (a) it is a linear multiplet with respect to its SU(2) indices, that is \( {D}_{\beta}^{\Big(i}{J}_{\alpha \left(m+1\right)\overset{\cdot }{\alpha}\left(n+1\right)}^{jk\Big)}=0 \) and \( {\overline{D}}_{\dot{\beta}}^{\Big(i}{J}_{\alpha \left(m+1\right)\overset{\cdot }{\alpha}\left(n+1\right)}^{jk\Big)}=0 \); and (b) it is conserved, \( {\partial}^{\beta \overset{\cdot }{\beta }}{J}_{\beta \alpha (m)\overset{\cdot }{\beta}\overset{\cdot }{\alpha }(n)}^{ij}=0 \). Realisations of the conformal supercurrents \( {J}_{\alpha (s)\overset{\cdot }{\alpha }(s)} \), with s = 0, 1, …, are naturally provided by a massless hypermultiplet and a vector multiplet. It turns out that such supercurrents and their linear descendants \( {J}_{\alpha \left(s+1\right)\overset{\cdot }{\alpha}\left(s+1\right)}^{ij} \) do not occur in the harmonic-superspace framework recently described by Buchbinder, Ivanov and Zaigraev. Making use of a massive hypermultiplet, we derive non-conformal higher-spin \( \mathcal{N} \) = 2 supercurrent multiplets. Additionally, we derive the higher symmetries of the kinetic operators for both a massive and massless hypermultiplet. Building on this analysis, we sketch the construction of higher-derivative gauge transformations for the off-shell arctic multiplet Υ(1), which are expected to be vital in the framework of consistent interactions between Υ(1) and superconformal higher-spin gauge multiplets.
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S.M. Kuzenko and E.S.N. Raptakis, Extended superconformal higher-spin gauge theories in four dimensions, JHEP 12 (2021) 210 [arXiv:2104.10416] [INSPIRE].
M.F. Sohnius, The multiplet of currents for N = 2 extended supersymmetry, Phys. Lett. B 81 (1979) 8 [INSPIRE].
P.S. Howe, K.S. Stelle and P.K. Townsend, Supercurrents, Nucl. Phys. B 192 (1981) 332 [INSPIRE].
E. Bergshoeff, M. de Roo and B. de Wit, Extended conformal supergravity, Nucl. Phys. B 182 (1981) 173 [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].
D. Butter and S.M. Kuzenko, N = 2 supergravity and supercurrents, JHEP 12 (2010) 080 [arXiv:1011.0339] [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, On the off-shell massive hypermultiplets, Class. Quant. Grav. 14 (1997) L157 [hep-th/9704002] [INSPIRE].
D. Butter and S.M. Kuzenko, N = 2 AdS supergravity and supercurrents, JHEP 07 (2011) 081 [arXiv:1104.2153] [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].
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. Buchbinder, E. Ivanov and N. Zaigraev, \( \mathcal{N} \) = 2 higher spins: superfield equations of motion, the hypermultiplet supercurrents, and the component structure, JHEP 03 (2023) 036 [arXiv:2212.14114] [INSPIRE].
I. Buchbinder, E. Ivanov and N. Zaigraev, Unconstrained off-shell superfield formulation of 4D, \( \mathcal{N} \) = 2 supersymmetric higher spins, JHEP 12 (2021) 016 [arXiv:2109.07639] [INSPIRE].
I. Buchbinder, E. Ivanov and N. Zaigraev, Off-shell cubic hypermultiplet couplings to \( \mathcal{N} \) = 2 higher spin gauge superfields, JHEP 05 (2022) 104 [arXiv:2202.08196] [INSPIRE].
C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18 (1978) 3624 [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].
J. Hutomo and S.M. Kuzenko, Non-conformal higher spin supercurrents, Phys. Lett. B 778 (2018) 242 [arXiv:1710.10837] [INSPIRE].
J.-H. Park, Superconformal symmetry and correlation functions, Nucl. Phys. B 559 (1999) 455 [hep-th/9903230] [INSPIRE].
S.M. Kuzenko and E.S.N. Raptakis, Symmetries of supergravity backgrounds and supersymmetric field theory, JHEP 04 (2020) 133 [arXiv:1912.08552] [INSPIRE].
D. Hutchings, Superspin projection operators and off-shell higher-spin supermultiplets on Minkowski and anti-de Sitter superspace, Ph.D. Thesis, University of Western Australia, Australia (2023).
P.S. Howe and U. Lindström, Notes on super Killing tensors, JHEP 03 (2016) 078 [arXiv:1511.04575] [INSPIRE].
P.S. Howe and U. Lindström, Some remarks on (super)-conformal Killing-Yano tensors, JHEP 11 (2018) 049 [arXiv:1808.00583] [INSPIRE].
P.S. Howe and U. Lindström, Super-Laplacians and their symmetries, JHEP 05 (2017) 119 [arXiv:1612.06787] [INSPIRE].
P.S. Howe and G.G. Hartwell, A superspace survey, Class. Quant. Grav. 12 (1995) 1823 [INSPIRE].
D. Butter, N = 2 conformal superspace in four dimensions, JHEP 10 (2011) 030 [arXiv:1103.5914] [INSPIRE].
S.M. Kuzenko, E.S.N. Raptakis and G. Tartaglino-Mazzucchelli, Covariant superspace approaches to \( \mathcal{N} \) = 2 supergravity, arXiv:2211.11162 [INSPIRE].
F. Gonzalez-Rey et al., Feynman rules in N = 2 projective superspace. I: Massless hypermultiplets, Nucl. Phys. B 516 (1998) 426 [hep-th/9710250] [INSPIRE].
S.M. Kuzenko, Lectures on nonlinear sigma-models in projective superspace, J. Phys. A 43 (2010) 443001 [arXiv:1004.0880] [INSPIRE].
P. Breitenlohner and M.F. Sohnius, Superfields, auxiliary fields, and tensor calculus for N = 2 extended supergravity, Nucl. Phys. B 165 (1980) 483 [INSPIRE].
P. Breitenlohner and M.F. Sohnius, An almost simple off-shell version of SU(2) Poincare supergravity, Nucl. Phys. B 178 (1981) 151 [INSPIRE].
A. Galperin et al., Unconstrained N = 2 matter, Yang-Mills and supergravity theories in harmonic superspace, Class. Quant. Grav. 1 (1984) 469 [Erratum ibid. 2 (1985) 127] [INSPIRE].
A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic Superspace, Cambridge University Press, Cambridge, U.K. (2001).
S.M. Kuzenko, M. Ponds and E.S.N. Raptakis, Conformal interactions between matter and higher-spin (super)fields, Fortsch. Phys. 71 (2023) 2200157 [arXiv:2208.07783] [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].
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].
S. Ferrara and B. Zumino, Transformation properties of the supercurrent, Nucl. Phys. B 87 (1975) 207 [INSPIRE].
S. Ferrara, J. Wess and B. Zumino, Supergauge multiplets and superfields, Phys. Lett. B 51 (1974) 239 [INSPIRE].
S.M. Kuzenko, U. Lindström, E.S.N. Raptakis and G. Tartaglino-Mazzucchelli, Symmetries of \( \mathcal{N} \) = (1, 0) supergravity backgrounds in six dimensions, JHEP 03 (2021) 157 [arXiv:2012.08159] [INSPIRE].
U. Lindström and M. Roček, N = 2 super Yang-Mills theory in projective superspace, Commun. Math. Phys. 128 (1990) 191 [INSPIRE].
S.M. Kuzenko, On superconformal projective hypermultiplets, JHEP 12 (2007) 010 [arXiv:0710.1479] [INSPIRE].
S.M. Kuzenko and G. Tartaglino-Mazzucchelli, Five-dimensional superfield supergravity, Phys. Lett. B 661 (2008) 42 [arXiv:0710.3440] [INSPIRE].
Acknowledgments
We are grateful to Michael Ponds for useful discussions. The work of SK is supported in part by the Australian Research Council, project No. DP200101944. The work of ER is supported by the Hackett Postgraduate Scholarship UWA, under the Australian Government Research Training Program.
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Kuzenko, S.M., Raptakis, E.S.N. On higher-spin \( \mathcal{N} \) = 2 supercurrent multiplets. J. High Energ. Phys. 2023, 56 (2023). https://doi.org/10.1007/JHEP05(2023)056
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DOI: https://doi.org/10.1007/JHEP05(2023)056