Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime

[en] Nonabelian Fradkin-Vasiliev cubic interactions for dual-graviton-like gauge fields with gravity and themselves are constructed in anti-de Sitter spacetime. The Young diagrams of gauge potentials have shapes of 'tall-hooks', i.e. two columns the second of height one. The underlying nonabelian algebra is a Clifford algebra with the anti-de Sitter signature. We also discuss the universal enveloping realization of higher-spin algebras, showing that there is a one-parameter family of algebras compatible with unitarity, which is reminiscent of 3d deformed oscillators.

Research center :

AGIF - Algèbre, Géométrie et Interactions fondamentales

Disciplines :

Physics

Author, co-author :

Boulanger, Nicolas ; Université de Mons > Faculté des Sciences > Mécanique et gravitation

Skvortsov, Evgeny

Language :

English

Title :

Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime

Publication date :

13 September 2011

Journal title :

Journal of High Energy Physics

ISSN :

1126-6708

Publisher :

Springer, Heidelberg, Germany

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi UMONS :

since 15 January 2012

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Bibliography

E.S. Fradkin and M.A. Vasiliev, On the Gravitational Interaction of Massless Higher Spin Fields, Phys. Lett. B 189 (1987) 89 [SPIRES].
E.S. Fradkin and M.A. Vasiliev, Cubic Interaction in Extended Theories of Massless Higher Spin Fields, Nucl. Phys. B 291 (1987) 141 [SPIRES].
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3+1)-dimensions, Phys. Lett. B 243 (1990) 378 [SPIRES].
M.A. Vasiliev, More on equations of motion for interacting massless fields of all spins in (3+1)-dimensions, Phys. Lett. B 285 (1992) 225 [SPIRES].
M.A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS(d), Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [SPIRES].
X. Bekaert, N. Boulanger and P. Sundell, How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples, arXiv:1007.0435 [SPIRES].
M.A. Vasiliev, Higher spin symmetries, star-product and relativistic equations in AdS space, hep-th/0002183 [SPIRES].
M.A. Vasiliev, Higher spin gauge theories in various dimensions, Fortsch. Phys. 52 (2004) 702 [hep-th/0401177] [SPIRES].
X. Bekaert, S. Cnockaert, C. Iazeolla and M.A. Vasiliev, Nonlinear higher spin theories in various dimensions, hep-th/0503128 [SPIRES].
D.J. Gross, High-Energy Symmetries of String Theory, Phys. Rev. Lett. 60 (1988) 1229 [SPIRES].
D. Polyakov, Interactions of Massless Higher Spin Fields From String Theory, Phys. Rev. D 82 (2010) 066005 [arXiv:0910.5338] [SPIRES].
D. Polyakov, Gravitational Couplings of Higher Spins from String Theory, Int. J. Mod. Phys. A 25 (2010) 4623 [arXiv:1005.5512] [SPIRES].
D. Polyakov, A String Model for AdS Gravity and Higher Spins, arXiv:1106.1558 [SPIRES].
A. Sagnotti and M. Taronna, String Lessons for Higher-Spin Interactions, Nucl. Phys. B 842 (2011) 299 [arXiv:1006.5242] [SPIRES].
X. Bekaert and N. Boulanger, On geometric equations and duality for free higher spins, Phys. Lett. B 561 (2003) 183 [hep-th/0301243] [SPIRES].
P. de Medeiros and C. Hull, Geometric second order field equations for general tensor gauge fields, JHEP 05 (2003) 019 [hep-th/0303036] [SPIRES].
P. de Medeiros, Massive gauge-invariant field theories on spaces of constant curvature, Class. Quant. Grav. 21 (2004) 2571 [hep-th/0311254] [SPIRES].
K.B. Alkalaev, O.V. Shaynkman and M.A. Vasiliev, On the frame-like formulation of mixed-symmetry massless fields in (A)dS(d), Nucl. Phys. B 692 (2004) 363 [hep-th/0311164] [SPIRES].
A. Sagnotti and M. Tsulaia, On higher spins and the tensionless limit of string theory, Nucl. Phys. B 682 (2004) 83 [hep-th/0311257] [SPIRES].
K.B. Alkalaev, O.V. Shaynkman and M.A. Vasiliev, Lagrangian formulation for free mixed-symmetry bosonic gauge fields in (A)dS(d), JHEP 08 (2005) 069 [hep-th/0501108] [SPIRES].
K.B. Alkalaev, O.V. Shaynkman and M.A. Vasiliev, Frame-like formulation for free mixed-symmetry bosonic massless higher-spin fields in AdS(d), hep-th/0601225 [SPIRES].
X. Bekaert and N. Boulanger, Tensor gauge fields in arbitrary representations of GL(D,R). II: Quadratic actions, Commun. Math. Phys. 271 (2007) 723 [hep-th/0606198] [SPIRES].
A. Fotopoulos and M. Tsulaia, Interacting Higher Spins and the High Energy Limit of the Bosonic String, Phys. Rev. D 76 (2007) 025014 [arXiv:0705.2939] [SPIRES].
I.L. Buchbinder, V.A. Krykhtin and H. Takata, Gauge invariant Lagrangian construction for massive bosonic mixed symmetry higher spin fields, Phys. Lett. B 656 (2007) 253 [arXiv:0707.2181] [SPIRES].
A.A. Reshetnyak, On Lagrangian formulations for mixed-symmetry HS fields on AdS spaces within BFV-BRST approach, arXiv:0809.4815 [SPIRES].
E.D. Skvortsov, Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space, Nucl. Phys. B 808 (2009) 569 [arXiv:0807.0903] [SPIRES].
Y.M. Zinoviev, Toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields, Nucl. Phys. B 812 (2009) 46 [arXiv:0809.3287] [SPIRES].
A. Campoleoni, D. Francia, J. Mourad and A. Sagnotti, Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields, Nucl. Phys. B 815 (2009) 289 [arXiv:0810.4350] [SPIRES].
N. Boulanger, C. Iazeolla and P. Sundell, Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism, JHEP 07 (2009) 013 [arXiv:0812.3615] [SPIRES].
Boulanger, N., Iazeolla, C., Sundell, P., Unfolding mixed-symmetry fields in AdS and the BMV conjecture: II. Oscillator realization. J. High Energy Phys., 0907, 2009, 014 arXiv:0812.4438.
A. Campoleoni, D. Francia, J. Mourad and A. Sagnotti, Unconstrained Higher Spins of Mixed Symmetry. II. Fermi Fields, Nucl. Phys. B 828 (2010) 405 [arXiv:0904.4447] [SPIRES].
Y.M. Zinoviev, Towards frame-like gauge invariant formulation for massive mixed symmetry bosonic fields. II. General Young tableau with two rows, Nucl. Phys. B 826 (2010) 490 [arXiv:0907.2140] [SPIRES].
E.D. Skvortsov, Gauge fields in (A)dS within the unfolded approach: algebraic aspects, JHEP 01 (2010) 106 [arXiv:0910.3334] [SPIRES].
K.B. Alkalaev and M. Grigoriev, Unified BRST description of AdS gauge fields, Nucl. Phys. B 835 (2010) 197 [arXiv:0910.2690] [SPIRES].
E.D. Skvortsov and M.A. Vasiliev, Reducible multiplets of bosonic massless mixed-symmetry fields, to appear (2010).
E.S. Fradkin and R.R. Metsaev, A Cubic interaction of totally symmetric massless representations of the Lorentz group in arbitrary dimensions, Class. Quant. Grav. 8 (1991) L89 [SPIRES].
X. Bekaert, N. Boulanger and M. Henneaux, Consistent deformations of dual formulations of linearized gravity: A no-go result, Phys. Rev. D 67 (2003) 044010 [hep-th/0210278] [SPIRES].
N. Boulanger and S. Cnockaert, Consistent deformations of (p, p)-type gauge field theories, JHEP 03 (2004) 031 [hep-th/0402180] [SPIRES].
X. Bekaert, N. Boulanger and S. Cnockaert, No self-interaction for two-column massless fields, J. Math. Phys. 46 (2005) 012303 [hep-th/0407102] [SPIRES].
R.R. Metsaev, Cubic interaction vertices for massive and massless higher spin fields, Nucl. Phys. B 759 (2006) 147 [hep-th/0512342] [SPIRES].
R.R. Metsaev, Cubic interaction vertices for fermionic and bosonic arbitrary spin fields, arXiv:0712.3526 [SPIRES].
K. Alkalaev, FV-type action for AdS5 mixed-symmetry fields, JHEP 03 (2011) 031 [arXiv:1011.6109] [SPIRES].
Y.M. Zinoviev, Gravitational cubic interactions for a massive mixed symmetry gauge field, arXiv:1107.3222 [SPIRES].
N. Boulanger, E.D. Skvortsov and Y.M. Zinoviev, Gravitational cubic interactions for a simple mixed-symmetry gauge field in AdS and flat backgrounds, arXiv:1107.1872 [SPIRES].
E. Sezgin and P. Sundell, Doubletons and 5D higher spin gauge theory, JHEP 09 (2001) 036 [hep-th/0105001] [SPIRES].
E. Sezgin and P. Sundell, Towards massless higher spin extension of D = 5, N = 8 gauged supergravity, JHEP 09 (2001) 025 [hep-th/0107186] [SPIRES].
Y.M. Zinoviev, On electromagnetic interactions for massive mixed symmetry field, JHEP 03 (2011) 082 [arXiv:1012.2706] [SPIRES].
E.S. Fradkin and M.A. Vasiliev, Candidate to the Role of Higher Spin Symmetry, Ann. Phys. 177 (1987) 63 [SPIRES].
S.E. Konshtein and M.A. Vasiliev, Massless representations and admissibility condition for higher spin superalgebras, Nucl. Phys. B 312 (1989) 402 [SPIRES].
M.A. Vasiliev, Higher spin superalgebras in any dimension and their representations, JHEP 12 (2004) 046 [hep-th/0404124] [SPIRES].
S.W. MacDowell and F. Mansouri, Unified Geometric Theory of Gravity and Supergravity, Phys. Rev. Lett. 38 (1977) 739 [SPIRES].
K.S. Stelle and P.C. West, Spontaneously broken de sitter symmetry and the gravitational holonomy group, Phys. Rev. D 21 (1980) 1466 [SPIRES].
S.F. Prokushkin and M.A. Vasiliev, Higher-spin gauge interactions for massive matter fields in 3D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [SPIRES].
M.A. Vasiliev, Higher spin algebras and quantization on the sphere and hyperboloid, Int. J. Mod. Phys. A 6 (1991) 1115 [SPIRES].
M. Henneaux and S.-J. Rey, Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [SPIRES].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [SPIRES].
A. Campoleoni, S. Fredenhagen and S. Pfenninger, Asymptotic W-symmetries in three-dimensional higher-spin gauge theories, arXiv:1107.0290 [SPIRES].
M.R. Gaberdiel and T. Hartman, Symmetries of Holographic Minimal Models, JHEP 05 (2011) 031 [arXiv:1101.2910] [SPIRES].
R.R. Metsaev, Massless mixed symmetry bosonic free fields in d- dimensional anti-de Sitter space-time, Phys. Lett. B 354 (1995) 78 [SPIRES].
E.D. Skvortsov, Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra, J. Phys. A 42 (2009) 385401 [arXiv:0904.2919] [SPIRES].
S. Deser and A. Waldron, Partial masslessness of higher spins in (A)dS, Nucl. Phys. B 607 (2001) 577 [hep-th/0103198] [SPIRES].
E.D. Skvortsov and M.A. Vasiliev, Geometric formulation for partially massless fields, Nucl. Phys. B 756 (2006) 117 [hep-th/0601095] [SPIRES].
L. Brink, R.R. Metsaev and M.A. Vasiliev, How massless are massless fields in AdS(d), Nucl. Phys. B 586 (2000) 183 [hep-th/0005136] [SPIRES].
M.A. Vasiliev, Cubic interactions of bosonic higher spin gauge fields in AdS5, Nucl. Phys. B 616 (2001) 106 [hep-th/0106200] [SPIRES].
K.B. Alkalaev, Two-column higher spin massless fields in AdS(d), Theor. Math. Phys. 140 (2004) 1253 [hep-th/0311212] [SPIRES].
V.E. Lopatin and M.A. Vasiliev, Free massless bosonic fields of arbitrary spin in d-dimensional de sitter space, Mod. Phys. Lett. A 3 (1988) 257 [SPIRES].
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] [SPIRES].
M.A. Vasiliev, On Conformal, SL(4,R) and Sp(8,R) Symmetries of 4d Massless Fields, Nucl. Phys. B 793 (2008) 469 [arXiv:0707.1085] [SPIRES].
C. Iazeolla and P. Sundell, A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations, JHEP 10 (2008) 022 [arXiv:0806.1942] [SPIRES].
X. Bekaert and M. Grigoriev, Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons, SIGMA 6 (2010) 038 [arXiv:0907.3195] [SPIRES].
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] [SPIRES].
M.A. Vasiliev, Consistent equations for interacting massless fields of all spins in the first order in curvatures, Annals Phys. 190 (1989) 59 [SPIRES].
S.E. Konstein and M.A. Vasiliev, Extended higher spin superalgebras and their massless representations, Nucl. Phys. B 331 (1990) 475 [SPIRES].
M.A. Vasiliev, Higher spin gauge theories: Star-product and AdS space, hep-th/9910096 [SPIRES].
M. Günaydin and D. Minic, Singletons, doubletons and M-theory, Nucl. Phys. B 523 (1998) 145 [hep-th/9802047] [SPIRES].
M. Flato and C. Fronsdal, One Massless Particle Equals Two Dirac Singletons: Elementary Particles in a Curved Space. 6, Lett. Math. Phys. 2 (1978) 421 [SPIRES].
F.A. Dolan, Character formulae and partition functions in higher dimensional conformal field theory, J. Math. Phys. 47 (2006) 062303 [hep-th/0508031] [SPIRES].
B. Feigin, The Lie algebras gl(λ) and cohomologies of Lie algebras of differential operators, Russ. Math. Surv. 43 (1988) 169.
D.P. Sorokin and M.A. Vasiliev, Reducible higher-spin multiplets in flat and AdS spaces and their geometric frame-like formulation, Nucl. Phys. B 809 (2009) 110 [arXiv:0807.0206] [SPIRES].
D.S. Ponomarev and M.A. Vasiliev, Frame-Like Action and Unfolded Formulation for Massive Higher-Spin Fields, Nucl. Phys. B 839 (2010) 466 [arXiv:1001.0062] [SPIRES].
N. Boulanger and E. Skvortsov, in preparation.
M. Vasiliev, to appear.