Supersymmetry at BLTP: Recent progress

I. L. Buchbinder; E. A. Ivanov

doi:10.54546/NaturalSciRev.200707

Additional data

Submitted: 30.03.2026; Accepted: 04.06.2026; Published 19.06.2026;

Views: 0; Downloaded: 0

How to Cite

I. L. Buchbinder, E. A. Ivanov "Supersymmetry at BLTP: Recent progress" Natural Sci. Rev. 3 200707 (2026)
https://doi.org/10.54546/NaturalSciRev.200707

I. L. Buchbinder^1,a, E. A. Ivanov^1,b

¹Joint Institute for Nuclear Research, 141980, Dubna, Russia

^abuchbinder@theor.jinr.ru
^beivanov@theor.jinr.ru

DOI: 10.54546/NaturalSciRev.200707

Topics: Physics , Mathematical physics , 70th anniversary of JINR

PDF

Abstract

Ten years ago, in a paper [1], a brief historical survey of the research activity in the Sector “Supersymmetry” at the Bogoliubov Laboratory of Theoretical Physics (BLTP) for more than 50 years of its existence has been given. Here, in commemoration of the 70th jubilee of the Joint Institute for Nuclear Research, we review some recent sound advancements in this area. Specifically, we consider the issues of constructing the superfield quantum effective actions in 6D, N = (1, 0) supersymmetry and off-shell unconstrained superfield formulations of N = 2 higher spins. In both cases, the harmonic superspace approach plays the decisive role.

Acknowledgements

The authors are grateful to Academician V. A. Matveev for the suggestion to prepare this review and to S. A. Fedoruk for useful remarks. We thank B. S. Merzlikin, K. V. Stepanyantz, and N. M. Zaigraev for a close collaboration on the topics overviewed here.

References

[1] E. A. Ivanov, Gauge fields, nonlinear realizations, superymmetry, Phys. Part. Nucl. 47 (2016) 4, 508–539; arXiv:1604.01379 [hep-th].

[2] V. I. Ogievetsky, I. V. Polubarinov, The notoph and its possible interactions, Yad. Fiz. 4 (1966) 216–223 [Sov. J. Nucl. Phys. 4 (1967) 156–161].

[3] V. I. Ogievetsky, Infinite-dimensional algebra of general covariance group as the closure of finite-dimensional algebras of conformal and linear groups, Lett. Nuovo Cim. 8 (1973) 988–990.

[4] A. B. Borisov, V. I. Ogievetsky, Theory of dynamical affine and conformal symmetries as gravity theory, Teor. Mat. Fiz. 21 (1974) 329–342 [Theor. Math. Phys. 21 (1975) 1179–1188].

[5] E. A. Ivanov, V. I. Ogievetsky, The inverse Higgs phenomenon in nonlinear realizations, Teor. Mat. Fiz. 25 (1975) 164–177.

[6] V. Ogievetsky, E. Sokatchev, Structure of supergravity group, Phys. Lett. B 79 (1978) 222–224.

[7] V. Ogievetsky, E. Sokatchev, The gravitational axial superfield and the formalism of differential geometry, Yad. Fiz. 31 (1980) 821–840 [Sov. J. Nucl. Phys. 31 (1980) 424].

[8] E. A. Ivanov, A. A. Kapustnikov, General relationship between linear and nonlinear realizations of supersymmetry, J. Phys. A 11 (1978) 2375–2384.

[9] E. A. Ivanov, A. A. Kapustnikov, The nonlinear realization structure of models with spontaneously broken supersymmetry, J. Phys. G 8 (1982) 167–191.

[10] A. Galperin, E. Ivanov, V. Ogievetsky, Grassmann analyticity and extended supersymmetry, Pis’ma ZhETF 33 (1981) 176–181 [JETP Lett. 33 (1981) 168–172].

[11] A. Galperin, E. Ivanov, V. Ogievetsky, E. Sokatchev, Harmonic superspace: Key to N = 2 supersymmetric theories, Pis’ma ZhETF 40 (1984) 155–158 [JETP Lett. 40 (1984) 912–916].

[12] A. Galperin, E. Ivanov, S. Kalitzin, V. Ogievetsky, E. Sokatchev, Unconstrained N = 2 matter, Yang–Mills and supergravity theories in harmonic superspace, Class. Quant. Grav. 1 (1984) 469–498; Class. Quant. Grav. 2 (1985) 127 E.

[13] A. Galperin, E. Ivanov, S. Kalitzin, V. Ogievetsky, E. Sokatchev, Unconstrained off-shell N = 3 supersymmetric Yang–Mills theory, Class. Quant. Grav. 2 (1985) 155–166.

[14] A. Galperin, E. Ivanov, S. Kalitzin, V. Ogievetsky, E. Sokatchev, N = 3 supersymmetric gauge theory, Phys. Lett. B 151 (1985) 215–218.

[15] A. S. Galperin, E. A. Ivanov, V. I. Ogievetsky, E. S. Sokatchev, Harmonic superspace, Cambridge University Press 2001, 306 p.

[16] C. Fronsdal, Massless fields with integer spin, Phys. Rev. D 18 (1978) 3624.

[17] J. Fang, C. Fronsdal, Massless fields with half integral spin, Phys. Rev. D 18 (1978) 3630.

[18] T. Courtright, Massless field supermultiplets with arbitrary spins, Phys. Lett. B 85 (1979) 2019.

[19] M. A. Vasiliev, Gauge form of description of massless fields with arbitrary spin, Yad. Fiz. 32 (1980) 855–861 (in Russian), Sov. J. Nucl. Phys. 32 (1980) 439.

[20] S. Kuzenko, A. Sibiryakov, V. Postnikov, Massless gauge superfields of higher half integer superspins, JETP Lett. 57 (1993) 534; S. Kuzenko, A. Sibiryakov, Massless gauge superfields of higher integer superspins, JETP Lett. 57 (1993) 539.

[21] S. M. Kuzenko, A. G. Sibiryakov, Free massless higher superspin superfields on the anti-de Sitter superspace, Phys. Atom. Nucl. 57 (1994) 1257–1267; arXiv:1112.4612 [hep-th].

[22] I. Buchbinder, E. Ivanov and N. Zaigraev, Unconstrained off-shell superfield formulation of 4D, N = 2 supersymmetric higher spins, JHEP 12 (2021) 016, arXiv:2109.07639 [hep-th].

[23] I. Buchbinder, E. Ivanov and N. Zaigraev, Off-shell cubic hypermultiplet couplings to N = 2 higher spin gauge superfields, JHEP 05 (2022) 104, arXiv:2202.08196 [hep-th].

[24] I. Buchbinder, E. Ivanov and N. Zaigraev, N = 2 higher spins: Superfield equations of motion, the hypermultiplet supercurrents, and the component structure, JHEP 03 (2023) 036, arXiv:2212.14114 [hep-th].

[25] I. Buchbinder, E. Ivanov and N. Zaigraev, N = 2 superconformal higher-spin multiplets and their hypermultiplet couplings, JHEP 08 (2024) 120, arXiv:2404.19016 [hep-th].

[26] E. Ivanov and N. Zaigraev, N = 2 AdS hypermultiplets in harmonic superspace, Phys. Lett. B 871 (2025) 139964, arXiv:2509.01406 [hep-th].

[27] E. Ivanov and N. Zaigraev, N = 2 superconformal gravitino in harmonic superspace, Phys. Lett. B 862 (2025) 139333, arXiv:2412.14822 [hep-th].

[28] R. Manvelyan, K. Mkrtchyan, W. Ruehl, A generating function for the cubic interactions of higher spin fields, Phys. Lett. B 696 (2011) 410–415, arXiv:1009.1054 [hep-th].

[29] R. R. Metsaev, Cubic interaction vertex for N = 1 arbitrary spin massless supermultiplet in flat space, JHEP 08 (2019) 130, arXiv:1905.11357 [hep-th].

[30] R. R. Metsaev, Cubic interactions for arbitrary spin N-extended massless supermultiplets in 4d flat space, JHEP 11 (2019) 084, arXiv:1909.05241 [hep-th].

[31] E. S. Fradkin and A. A. Tseytlin, Conformal supergravity, Phys. Rep. 119 (1985) 233–362.

[32] E. S. Fradkin, V. Y. Linetsky, Cubic interaction in conformal theory of integer higher spin fields in four-dimensional space-time, Phys. Lett. B 231 (1989) 97–106.

[33] E. S. Fradkin, V. Y. Linetsky, Superconformal higher spin theory in the cubic approximation, Nucl. Phys. B 350 (1991) 274–324.

[34] A. Y. Segal, Conformal higher spin theory, Nucl. Phys. B 664 (2003) 59–130, arXiv:hep-th/0207212 [hep-th].

[35] S. M. Kuzenko, R. Manvelyan, S. Theisen, Off-shell superconformal higher spin multiplets in four dimensions, JHEP 07 (2017) 034, arXiv:1701.00682 [hep-th].

[36] S. M. Kuzenko and E. S. N. Raptakis, Extended superconformal higher-spin gauge theories in four dimensions, JHEP 12 (2021) 210 arXiv:2104.10416 [hep-th].

[37] E. A. Ivanov, A. S. Sorin, Superfield formulation of OSp(1, 4) supersymmetry, J. Phys. A 13 (1980) 1159–1188.

[38] S. M. Kuzenko, G. Tartaglino-Mazzucchelli, Five-dimensional N = 1 AdS superspace: Geometry, off-shell multiplets and dynamics, Nucl. Phys. B 785 (2007) 34–73, arXiv:0704.1185 [hep-th].

[39] E. I. Buchbinder, S. M. Kuzenko, and I. B. Samsonov, Massless higher-spin supermultiplets in 5D harmonic superspace, JHEP 02 (2026) 122, arXiv:2509.06604 [hep-th].

[40] S. J. Gates, M. T. Grisaru, M. Rocek and W. Siegel, Superspace or one thousand and one lessons in supersymmetry, Front. Phys. 58 (1983) 1–548, arXiv:hep-th/0108200 [hep-th].

[41] I. Bandos, E. Ivanov, J. Lukierski, D. Sorokin, On the superconformal flatness of AdS superspaces, JHEP 06 (2002) 040, arXiv:hep-th/0205104 [hep-th].

[42] N. Zaigraev, N = 2 higher-spin supercurrents, Phys. Lett. B 858 (2024) 139056, arXiv:2408.00668 [hep-th].

[43] I. L. Buchbinder, E. A. Ivanov, M. B. Merzlikin, K. V. Stepanyantz, One-loop divergences in the 6D, N = (1, 0) Abelian gauge theory, Phys. Lett. B 763 (2016) 375, arXiv:1609.00975 [hep-th].

[44] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, One-loop divergences in 6D, N = (1, 0) SYM theory, JHEP 1701 (2017) 128, arXiv:1612.03190 [hep-th].

[45] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, Supergraph analysis of the one-loop divergences in 6D, N = (1, 0) and N = (1, 1) gauge theories, Nucl. Phys. B 921 (2017) 127, arXiv:1704.02530 [hep-th].

[46] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, Leading low-energy effective action in 6D,N = (1, 1) and N = (1, 1) SYM theory, JHEP 09 (2018) 039, arXiv:1711.03302 [hep-th].

[47] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, On the two-loop divergences of the 2-point hypermultiplet supergraphs for 6D, N = (1, 1) and N = (1, 1) SYM theory, Phys. Lett. B 778 (2018) 252, arXiv:1711.11514 [hep-th].

[48] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, Gauge dependence of the one-loop divergences in 6D, N = (1, 0) Abelian theory, Nucl. Phys. B 936 (2018) 638, arXiv:1808.08446 [hep-th].

[49] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, Harmonic superspace approach to the effective action in six-dimensional supersymmetric gauge theories, Symmetry 11 (2019) 1, arXiv:1812.02681 [hep-th].

[50] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, On gauge dependence of the one-loop divergences in 6D N = (1, 0) and N = (1, 1) SYM theories, Phys. Lett. B 798 (2019) 134957, arXiv:1907.12302 [hep-th].

[51] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, Low-energy 6D, N = (1, 1) SYM effective action beyond the leading approximation, Nucl. Phys. B 954 (2020) 114995, arXiv:1912.02634 [hep-th].

[52] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory, JHEP 08 (2020) 169, arXiv:2004.12657 [hep-th].

[53] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, The renormalization structure of 6D, N = (1, 0) supersymmetric higher-derivative gauge theory, Nucl. Phys. B 961 (2020) 115249, arXiv:2007.02843 [hep-th].

[54] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, On the two-loop divergences in 6D, N = (1, 1) SYM theory, Phys. Lett. B 820 (2021) 136516, arXiv:2104.14284 [hep-th].

[55] A. S. Budekhina, I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, On two-loop divergences in 6D, N = (1, 1) supergauge theory, Phys. Part. Nucl. Lett. 19 (2022) 666.

[56] I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz, On two-loop divergences of effective action in 6D, N = (1, 1) SYM theory, JHEP 05 (2023) 089, arXiv:2212.03766 [hep-th].

[57] C. V. Johnson, D-branes, Cambridge Univ. Press, 2006.

[58] K. Becker, M. Becker, J. H. Schwarz, String theory and M-theory, Cambridge Univ. Press, 2012.

[59] J. Bagger, N. Lambert, S. Mukhi, C. Papageorgakis, Multiple membranes in M-theory, Phys. Rep. 527 (2013) 1, arXiv:1203.3546 [hep-th].

[60] N. Seiberg, E. Witten, Comments on string dynamics in six dimensions, Nucl. Phys. B 471 (1996) 121, arXiv:hep th/9603003 [hep-th].

[61] N. Seiberg, New theories in six dimensions and matrix description of M-theory on T5 and T5/Z2, Phys. Lett. B 408 (1997) 98, arXiv:hep-th/9705221 [hep-th].

[62] E. S. Fradkin, A. A. Tseytlin, Quantum properties of higher dimensional and dimensionally reduced supersymmetric theories, Nucl. Phys. B 227 (1983) 252.

[63] P. S. Howe, K. S. Stelle, Ultraviolet divergences in higher dimensional supersymmetric Yang–Mills theories, Phys. Lett. B 137 (1984) 175.

[64] N. Marcus, A. Sagnotti, A test of finiteness predictions for supersymmetric theories, Phys. Lett. B 135 (1984) 85.

[65] N. Marcus, A. Sagnotti, The ultraviolet behavior of N = 4 Yang–Mills and the power counting of extended super-space, Nucl. Phys. B 256 (1985) 77.

[66] P. S. Howe, K. S. Stelle, Supersymmetry counterterms revisited, Phys. Lett. B 554 (2003) 190, arXiv:hep-th/0211279 [hep-th].

[67] D. I. Kazakov, Ultraviolet fixed points in gauge and SUSY field theories in extra dimensions, JHEP 03 (2003) 020, arXiv:hep-th/0209100 [hep-th].

[68] L. V. Bork, D. I. Kazakov, M. V. Kompaniets, D. M. Tolkachev, D. E. Vlasenko, Divergences in maximal supersymmetric Yang–Mills theories in diverse dimensions, JHEP 11 (2015) 059, arXiv:1508.05570[hep-th].

[69] P. S. Howe, G. Sierra, P. K. Townsend, Supersymmetry in six dimensions, Nucl. Phys. B 221 (1983) 331.

[70] P. S. Howe, K. S. Stelle, P. C. West, N = 1 d = 6 harmonic superspace, Class. Quant. Grav. 2 (1985) 815.

[71] B. M. Zupnik, Six-dimensional supergauge theories in the harmonic superspace, Sov. J. Nucl. Phys. 44 (1986) 512 [Yad. Fiz. 44 (1986) 794].

[72] G. Bossard, E. Ivanov and A. Smilga, Ultraviolet behavior of 6D supersymmetric Yang–Mills theories and harmonic superspace, JHEP 12 (2015) 085, arXiv:1509.08027[hep-th].

[73] E. A. Ivanov, A. V. Smilga, B. M. Zupnik, Renormalizable supersymmetric gauge theory in six dimensions, Nucl. Phys. B 726 (2005) 131, arXiv:0505082 [hep-th].

[74] A. Casarin, A. A. Tseytlin, One-loop β-function in 4-derivative gauge theory in 6 dimensions, JHEP 08 (2019) 159, arXiv:1907.02501 [hep-th].

[75] A. Giveon, D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys. 71 (1999) 981, arXiv:hep-th/9802067 [hep-th].

[76] R. Blumenhagen, B. Kors, D. Lüst, S. Stieberger, Four-dimensional string compactifications with D-branes, orbifolds and fluxes, Phys. Rep. 445 (2007) 1–193, arXiv:hep-th/0610327 [hep-th].