Abstract
Sp(2M) invariant field equations in the space ℳ M with symmetric matrix coordinates are classified. Analogous results are obtained for Minkowski-like subspaces of ℳ M which include usual 4d Minkowski space as a particular case. The constructed equations are associated with the tensor products of the Fock (singleton) representation of Sp(2M) of any rank r. The infinite set of higher-spin conserved currents multilinear in rank-one fields in ℳ M is found. The associated conserved charges are supported by \( \mathrm{r}M-\frac{\mathrm{r}\left(\mathrm{r}-1\right)}{2} \)-dimensional differential forms in ℳ M , that are closed by virtue of the rank-2r field equations. The cohomology groups H p(σ r− ) with all p and r, which determine the form of appropriate gauge fields and their field equations, are found both for ℳ M and for its Minkowski-like subspace.
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References
C. Fronsdal, Massless Particles, Ortosymplectic Symmetry and Another Type of Kaluza-Klein Theory, Preprint UCLA/85/TEP/10, in Mathematical Physics Studies. Vol. 8: Essays on Supersymmetry, Reidel Publishing, Dordrecht Netherlands (1986).
I.A. Bandos and J. Lukierski, Tensorial central charges and new superparticle models with fundamental spinor coordinates, Mod. Phys. Lett. A 14 (1999) 1257 [hep-th/9811022] [INSPIRE].
I.A. Bandos, J. Lukierski and D.P. Sorokin, Superparticle models with tensorial central charges, Phys. Rev. D 61 (2000) 045002 [hep-th/9904109] [INSPIRE].
M.A. Vasiliev, Conformal higher spin symmetries of 4 − d massless supermultiplets and osp(L,2M) invariant equations in generalized (super)space, Phys. Rev. D 66 (2002) 066006 [hep-th/0106149] [INSPIRE].
O.A. Gelfond and M.A. Vasiliev, Higher rank conformal fields in the Sp(2M) symmetric generalized space-time, Theor. Math. Phys. 145 (2005) 1400 [hep-th/0304020] [INSPIRE].
M.A. Vasiliev, Higher spin conserved currents in Sp(2M) symmetric space-time, Russ. Phys. J. 45 (2002) 670 [hep-th/0204167] [INSPIRE].
M.A. Vasiliev, Relativity, causality, locality, quantization and duality in the Sp(2M) invariant generalized space-time, hep-th/0111119 [INSPIRE].
I. Bandos, X. Bekaert, J.A. de Azcarraga, D. Sorokin and M. Tsulaia, Dynamics of higher spin fields and tensorial space, JHEP 05 (2005) 031 [hep-th/0501113] [INSPIRE].
M.A. Vasiliev, Consistent equations for interacting massless fields of all spins in the first order in curvatures, Annals Phys. 190 (1989) 59 [INSPIRE].
O.A. Gelfond and M.A. Vasiliev, Operator algebra of free conformal currents via twistors, Nucl. Phys. B 876 (2013) 871 [arXiv:1301.3123] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
E. Sezgin and P. Sundell, Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, JHEP 07 (2005) 044 [hep-th/0305040] [INSPIRE].
S. Giombi and X. Yin, Higher spin gauge theory and holography: the three-point functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].
S. Giombi and X. Yin, Higher spins in AdS and twistorial holography, JHEP 04 (2011) 086 [arXiv:1004.3736] [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining Conformal Field Theories with A Higher Spin Symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav. 30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].
S. Giombi and X. Yin, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Minimal Model Holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [INSPIRE].
M.A. Vasiliev, Holography, Unfolding and Higher-Spin Theory, J. Phys. A 46 (2013) 214013 [arXiv:1203.5554] [INSPIRE].
K. Alkalaev, Mixed-symmetry tensor conserved currents and AdS/CFT correspondence, J. Phys. A 46 (2013) 214007 [arXiv:1207.1079] [INSPIRE].
V.E. Didenko and E.D. Skvortsov, Towards higher-spin holography in ambient space of any dimension, J. Phys. A 46 (2013) 214010 [arXiv:1207.6786] [INSPIRE].
R.R. Metsaev, CFT adapted approach to massless fermionic fields, AdS/CFT and fermionic conformal fields, arXiv:1311.7350 [INSPIRE].
O.A. Gelfond and M.A. Vasiliev, Unfolded Equations for Current Interactions of 4d Massless Fields as a Free System in Mixed Dimensions, J. Exp. Theor. Phys. 120 (2015) 484 [arXiv:1012.3143] [INSPIRE].
H. Elvang and Y.-t. Huang, Scattering Amplitudes, arXiv:1308.1697 [INSPIRE].
A.K. Aiston and H.R. Morton, Idempotents of Hecke algebras of type A, q-alg/9702017.
O.V. Shaynkman and M.A. Vasiliev, Scalar field in any dimension from the higher spin gauge theory perspective, Theor. Math. Phys. 123 (2000) 683 [hep-th/0003123] [INSPIRE].
X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [INSPIRE].
M. Günaydin and D. Minic, Singletons, doubletons and M-theory, Nucl. Phys. B 523 (1998) 145 [hep-th/9802047] [INSPIRE].
M. Günaydin, Unitary supermultiplets of OSp(1/32, R) and M-theory, Nucl. Phys. B 528 (1998) 432 [hep-th/9803138] [INSPIRE].
R. Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989) 539.
M.A. Vasiliev, Bosonic conformal higher-spin fields of any symmetry, Nucl. Phys. B 829 (2010) 176 [arXiv:0909.5226] [INSPIRE].
O.A. Gelfond and M.A. Vasiliev, Higher Spin Fields in Siegel Space, Currents and Theta Functions, JHEP 03 (2009) 125 [arXiv:0801.2191] [INSPIRE].
M.A. Vasiliev, Multiparticle extension of the higher-spin algebra, Class. Quant. Grav. 30 (2013) 104006 [arXiv:1212.6071] [INSPIRE].
N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, A. Postnikov and J. Trnka, On-Shell Structures of MHV Amplitudes Beyond the Planar Limit, JHEP 06 (2015) 179 [arXiv:1412.8475] [INSPIRE].
L.V. Bork and A.I. Onishchenko, Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N = 4 SYM, arXiv:1607.02320 [INSPIRE].
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Gelfond, O., Vasiliev, M. Higher-rank fields and currents. J. High Energ. Phys. 2016, 67 (2016). https://doi.org/10.1007/JHEP10(2016)067
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DOI: https://doi.org/10.1007/JHEP10(2016)067