Higher spins in harmonic superspace

E. A. Ivanov

Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 3, pp. 515-532

Résumé

We report on a recent progress in constructing off-shell $4$D, $\mathcal{N}=2$ supersymmetric integer higher-superspin theory in terms of unconstrained harmonic analytic gauge superfields and their cubic interaction with matter hypermultiplets. For even superspins, a new equivalent representation of the hypermultiplet couplings in terms of an analytic $\omega$ superfield is presented. It involves both cubic and quartic vertices.

Détail

Keywords: supersymmetry, harmonic superspace, higher spins.

Bibliographie

[1] M. A. Vasiliev, “Higher spin gauge theories in various dimensions”, Fortschr. Phys., 52:6–7 (2004), 702–717, arXiv: hep-th/0401177 | DOI | MR

[2] X. Bekaert, S. Cnockaert, C. Iazeolla, M. A. Vasiliev, “Nonlinear higher spin theories in various dimensions”, Proceedings of the First Solvay Workshop on Higher Spin Gauge Theories (Brussels, Belgium, 12–14 May, 2004), eds. R. Argurio, G. Barnich, G. Bonelli, M. Grigoriev, International Solvay Institutes for Physics and Chemistry, Brussels, 2006, 132–197, arXiv: hep-th/0503128

[3] X. Bekaert, N. Boulanger, P. Sundell, “How higher-spin gravity surpasses the spin-two barrier”, Rev. Mod. Phys., 84:3 (2012), 987–1009, arXiv: 1007.0435 | DOI

[4] A. Sagnotti, “Notes on strings and higher spins”, J. Phys. A: Math. Theor., 46:21 (2013), 214006, 29 pp., arXiv: 1112.4285 | DOI | MR

[5] V. E. Didenko, E. D. Skvortsov, Elements of Vasiliev theory, arXiv: 1401.2975

[6] X. Bekaert, N. Boulanger, A. Campoleoni, M. Chodaroli, D. Francia, M. Grigoriev, E. Sezgin, E. Skvortsov, Snowmass white paper: Higher spin gravity and higher spin symmetry, arXiv: 2205.01567

[7] C. Fronsdal, “Massless fields with integer spin”, Phys. Rev. D, 18:10 (1978), 3624–3629 | DOI

[8] J. Fang, C. Fronsdal, “Massless fields with half-integral spin”, Phys. Rev. D, 18:10 (1978), 3630–3633 | DOI

[9] T. Curtright, “Massless field supermultiplets with arbitrary spins”, Phys. Lett. B, 85:2–3 (1979), 219–224 | DOI

[10] M. A. Vasilev, “ “Kalibrovochnaya” forma opisaniya bezmassovykh nolei proizvolnogo spina”, YaF, 32:3 (1980), 855–861 | MR

[11] S. M. Kuzenko, V. V. Postnikov, A. G. Sibiryakov, “Bezmassovye kalibrovochnye superpolya vysshikh polutselykh superspinov”, Pisma v ZhETF, 57:9 (1993), 521–525; С. М. Кузенко, А. Г. Сибиряков, “Безмассовые калибровочные суперполя высших целых суперспинов”, Письма в ЖЭТФ, 57:9 (1993), 526–529; С. М. Кузенко, А. Г. Сибиряков, “Свободные безмассовые сверхспиновые сверхполя в сверхпространстве анти-де Ситтера”, ЯФ, 57:7 (1994), 1326–1337, arXiv: 1112.4612

[12] S. J. Gates, Jr., S. M. Kuzenko, A. G. Sibiryakov, “Towards a unified theory of massless superfields of all superspins”, Phys. Lett. B, 394:3–4 (1997), 343–353, arXiv: hep-th/9611193 | DOI | MR

[13] S. J. Gates, Jr., K. Koutrolikos, “On $4D$, $N=1$ massless gauge superfields of arbitrary superhelicity”, JHEP, 06 (2014), 098, 47 pp., arXiv: 1310.7385 | DOI

[14] K. Koutrolikos, “Superspace formulation of massive half-integer superspin”, JHEP, 03 (2021), 254, 23 pp., arXiv: 2012.12225 | DOI | MR

[15] I. Buchbinder, E. Ivanov, N. Zaigraev, “Unconstrained off-shell superfield formulation of $4D$, $\mathcal{N} = 2$ supersymmetric higher spins”, JHEP, 12 (2021), 016, 27 pp., arXiv: 2109.07639 | DOI | MR

[16] A. Galperin, E. Ivanov, V. Ogievetskii, E. Sokachev, Pisma v ZhETF, 40:4 (1984), 155–158, Garmonicheskoe superprostranstvo – klyuch k $N = 2$ supersimmetrichnym teoriyam

[17] A. S. Galperin, E. A. Ivanov, V. I. Ogievetsky, E. S. Sokatchev, Harmonic Superspace, Cambridge Univ. Press, Cambridge, 2001 | DOI | MR

[18] I. Buchbinder, E. Ivanov, N. Zaigraev, “Off-shell cubic hypermultiplet couplings to $\mathcal{N} = 2$ higher spin gauge superfields”, JHEP, 05 (2022), 104, 37 pp., arXiv: 2202.08196 | DOI | MR

[19] I. Buchbinder, E. Ivanov, N. Zaigraev, “Unconstrained $\mathcal{N} = 2$ higher-spin gauge superfields and their hypermultiplet couplings”, Phys. Part. Nucl. Lett., 20:3 (2023), 300–305, arXiv: 2211.09501 | DOI

[20] I. Buchbinder, E. Ivanov, N. Zaigraev, “$\mathcal{N} = 2$ higher spins: superfield equations of motion, the hypermultiplet supercurrents, and the component structure”, JHEP, 03 (2023), 036, 87 pp., arXiv: 2212.14114 | DOI | MR

[21] E. S. Fradkin, M. A. Vasiliev, “Minimal set of auxiliary fields and S-matrix for extended supergravity”, Lett. Nuovo Cimento, 25 (1979), 79–87 | DOI

[22] B. De Wit, J. W. van Holten, “Multiplets of linearized SO$(2)$ supergravity”, Nucl. Phys. B, 155:2 (1979), 530–542 | DOI | MR

[23] B. De Wit, J. W. van Holten, A. Van Proeyen, “Transformation rules of $N=2$ supergravity multiplets”, Nucl. Phys. B, 167:1–2 (1980), 186–204 | DOI | MR

[24] A. K. H. Bengtsson, I. Bengtsson, L. Brink, “Cubic interaction terms for arbitrary spin”, Nucl. Phys. B, 227:1 (1983), 31–40 ; “Cubic interaction terms for arbitrary extended supermultiplets”, 41–49 | DOI | DOI

[25] E. S. Fradkin, R. R. Metsaev, “A cubic interaction of totally symmetric massless representations of the Lorentz group in arbitrary dimensions”, Class. Quantum Grav., 8:4 (1991), L89–L94 | DOI | MR

[26] R. R. Metsaev, “Generating function for cubic interaction vertices of higher spin fields in any dimension”, Modern Phys. Lett. A, 8:25 (1993), 2413–2426 | DOI | MR

[27] R. Manvelyan, K. Mkrtchyan, W. Rühl, “General trilinear interaction for arbitrary even higher spin gauge fields”, Nucl. Phys. B, 836:3 (2010), 204–221, arXiv: ; “A generating function for the cubic interactions of higher spin fields”, Phys. Lett. B, 696:4 (2011), 410–415, arXiv: 1003.28771009.1054 | DOI | MR | DOI | MR

[28] A. Fotopoulos, N. Irges, A. C. Petkou, M. Tsulaia, “Higher spin gauge fields interacting with scalars: the Lagrangian cubic vertex”, JHEP, 10 (2007), 021, 27 pp., arXiv: 0708.1399 | DOI | MR

[29] X. Bekaert, E. Joung, J. Mourad, “On higher spin interactions with matter”, JHEP, 05 (2009), 126, 31 pp., arXiv: 0903.3338 | DOI

[30] M. V. Khabarov, Yu. M. Zinoviev, “Massless higher spin cubic vertices in flat four dimensional space”, JHEP, 08 (2020), 112, 21 pp., arXiv: 2005.09851 | DOI | MR

[31] M. V. Khabarov, Yu. M. Zinoviev, “Cubic interaction vertices for massless higher spin supermultiplets in $d = 4$”, JHEP, 02 (2021), 167, 17 pp., arXiv: 2012.00482 | DOI | MR

[32] I. L. Buchbinder, S. J. Gates, Jr., K. Koutrolikos, “Integer superspin supercurrents of matter supermultiplets”, JHEP, 05 (2019), 031, 18 pp., arXiv: 1811.12858 | DOI | MR

[33] A. Galperin, N. A. Ky, E. Sokatchev, “$\mathcal{N}=2$ supergravity in superspace: solution to the constraints”, Class. Quantum Grav., 4:5 (1987), 1235–1253 | MR

[34] S. M. Kuzenko, S. Theisen, “Correlation functions of conserved currents in $\mathcal N=2$ superconformal theory”, Class. Quant. Grav., 17:3 (2000), 665–696, arXiv: hep-th/9907107 | DOI | MR

[35] A. Galperin, E. Ivanov, V. Ogievetsky, E. Sokatchev, “$N=2$ supergravity in superspace: different versions and matter couplings”, Class. Quantum Grav., 4:5 (1987), 1255–1265 | DOI | MR

[36] S. M. Kuzenko, E. S. N. Raptakis, “Extended superconformal higher-spin gauge theories in four dimensions”, JHEP, 12 (2021), 210, 26 pp., arXiv: 2104.10416 | DOI | MR

[37] E. I. Buchbinder, J. Hutomo, S. M. Kuzenko, “Higher spin supercurrents in anti-de Sitter space”, JHEP, 09 (2018), 51 pp., arXiv: 1805.08055 | DOI | MR

[38] S. M. Kuzenko, M. Ponds, E. S. N. Raptakis, “Conformal interactions between matter and higher-spin (super)fields”, Fortsch. Phys., 71:1 (2023), 2200157, 31 pp., arXiv: 2208.07783 | DOI | MR

[39] S. M. Kuzenko, E. S. N. Raptakis, “On higher-spin $ \mathcal{N} = 2$ supercurrent multiplets”, JHEP, 05 (2023), 056, 20 pp., arXiv: 2301.09386 | DOI | MR

[40] E. Ivanov, $\mathcal N=2$ supergravities in harmonic superspace, arXiv: 2212.07925

[41] E. I. Bukhbinder, B. A. Ovrut, I. L. Bukhbinder, E. A. Ivanov, S. M. Kuzenko, “Nizkoenergeticheskoe effektivnoe deistvie v $N = 2$ supersimmetrichnykh teoriyakh polya”, EChAYa, 32:5 (2001), 1222–1264