Metric-like Lagrangian Formulations for Higher-Spin Fields of Mixed Symmetry

[en] We review the structure of local Lagrangians and field equations for free bosonic and fermionic gauge fields of mixed symmetry in flat space. These are first presented in a constrained setting extending the metric formulation of linearized gravity, and then the (γ-)trace constraints on fields and gauge parameters are eliminated via the introduction of auxiliary fields. We also display the emergence of Weyl-like symmetries in particular classes of models in low space-time dimensions.

Disciplines :

Physics

Author, co-author :

Campoleoni, Andrea

Language :

English

Title :

Metric-like Lagrangian Formulations for Higher-Spin Fields of Mixed Symmetry

Publication date :

23 April 2010

Journal title :

Rivista del Nuovo Cimento della Societa Italiana di Fisica

ISSN :

0393-697X

Publisher :

Societa Italiana di Fisica, Italy

Volume :

Pages :

123-253

Peer reviewed :

Peer reviewed

Available on ORBi UMONS :

since 04 December 2016

Statistics

Number of views

11 (0 by UMONS)

Number of downloads

0 (0 by UMONS)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

Bibliography

VENEZIANO G., "Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories", Nuovo Cimento A, 57 (1968) 190.
YONEYA T, "Quantum gravity and the zero slope limit of the generalized Virasoro model", Lett. Nuovo Cimento, 8 (1973) 951.
SCHERK J. and SCHWARZ J. H., "Dual Models For Nonhadrons,", Nucl. Phys. B, 81 (1974) 118.
GOROFF M. H. and SAGNOTTI A., "Quantum Gravity At Two Loops", Phys. Lett. B, 160 (1985) 81;
'The Ultraviolet Behavior Of Einstein Gravity", Nucl. Phys. B, 266 (1986) 709.
SAGNOTTI A. and SEVRIN A., "Strings, gravity and particle physics", Riv. Nuovo Cimento, 31 (2008) 423 [arXiv:hep-ex/0209011].
GREEN M. B., SCHWARZ J. H. and WITTEN E., Superstring Theory, 2 vols. (Cambridge University Press, Cambridge, UK) 1987;
POLCHINSKI J., String Theory, 2 vols. (Cambridge University Press, Cambridge, UK) 1998;
ZWIEBACH B., A First Course in String Theory (Cambridge University Press, Cambridge, UK) 2004;
BECKER K., BECKER M. and SCHWARZ J. H., String Theory and M-theory: A Modern Introduction (Cambridge University Press, Cambridge, UK) 2007;
KIRITSIS E., String Theory in a Nutshell (Princeton University Press, Princeton, NJ, USA) 2007.
KATO M. and OGAWA K., "Covariant Quantization Of String Based On Brs Invariance", Nucl. Phys. B, 212 (1983) 443;
SIEGEL W., "Classical Superstring Mechanics", Nucl. Phys. B, 263 (1986) 93;
SIEGEL W. and ZWIEBACH B., "Gauge String Fields", Nucl. Phys. B, 263 (1986) 105;
BANKS T. and PESKIN M. E., "Gauge Invariance Of String Fields", Nucl. Phys. B, 264 (1986) 513;
OHTA N., "Covariant Quantization Of Superstring s Based On Brs Invariance", Phys. Rev. D, 33 (1986) 1681,
"Covariant Second Quantization of Superstrings", Phys. Rev. Lett., 56 (1986) 440; 1316(E);
NEVEU A., NICOLAI H. and WEST P. C., "Gauge Covariant Local Formulation Of Free Strings And Superstrings", Nucl. Phys. B, 264 (1986) 573;
NEVEU A. and WEST P. C., "Gauge Covariant Local Formulation Of Bosonic Strings", Nucl. Phys. B, 268 (1986) 125.
WITTEN E., "Noncommutative Geometry And String Field Theory", Nucl. Phys. B, 268 (1986) 253.
B. ZWIEBACH, "Closed string field theory: Quantum action and the B-V master equation", Nucl. Phys. B, 390 (1993) 33 [arXiv:hep-th/9206084].
CREMMER E., JULIA B. and SCHERK J., "Supergravity theory in 11 dimensions", Phys. Lett. B, 76 (1978) 409;
CREMMER E. and JULIA B., "The SO(8) Supergravity", Nucl. Phys. B, 159 (1979) 141.
BERN Z., CARRASCO J. J., DIXON L. J., JOHANSSON H. and ROIBAN R., "The Ultraviolet Behavior of N =8 Supergravity at Four Loops", arXiv:0905.2326 [hep-th].
BEKAERT X., BUCHBINDER I. L., PASHNEV A. and TSULAIA M., "On higher spin theory: Strings, BRST, dimensional reductions", Class. Quantum Grav., 21 (2004) S1457 [arXiv:hep-th/0312252];
SOROKIN D., "Introduction to the classical theory of higher spins", AIP Conf Proc, 767 (2005) 172 [arXiv:hep-th/0405069];
BOUATTA N., COMPERE G. and SAGNOTTI A., "An introduction to free higher-spin fields", arXivihepth/0409068;
SAGNOTTI A., SEZGIN E. and SUNDELL P., "On higher spins with a strong Sp(2,R) condition", arXiv:hep-th/0501156;
FOTOPOULOS A. and TSULAIA M., "Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation", arXiv:0805.1346 [hep-th].
VASILIEV M. A., "Higher-spin gauge theories in four, three and two dimensions", Int. J. Mod. Phys. D, 5 (1996) 763 [arXiv:hep-th/9611024];
"Higher spin gauge theories in various dimensions", Fortschr. Phys., 52 (2004) 702 [arXiv:hep-th/0401177];
BEKAERT X., CNOCKAERT S., IAZEOLLA C. and VASILIEV M. A., "Nonlinear higher spin theories in various dimensions", arXiv:hep-th/0503128.
MAJORANA E., "Teoria relativistica di particelle con momento intrinseco arbitrario", Nuovo Cimento, 9 (1932) 335 (English translation in Bassani G.F. (Editor),
"Ettore Majorana Scientific Papers" (SIF, Bologna; Springer, Berlin) 2006).
DlRAC P. A. M., "Relativistic wave equations", Proc. R. Soc. London, Ser. A, 155 (1936) 447.
WIGNER E. P., "On Unitary Representations Of The Inhomogeneous Lorentz Group", Ann. Math., 40 (1939) 149
(Nucl. Phys. Proc. Suppl., 6 (1989) 9).
BARGMANN V. and WIGNER E. P., "Group Theoretical Discussion Of Relativistic Wave Equations", Proc. Natl. Acad. Sci. U.S.A., 34 (1948) 211.
FlERZ M., "Uber die relativistiche; theorie kraftefreier teilchen mit beliebigem spin", Helv. Phys. Acta, 12 (1939) 3.
FlERZ M. and PAULI W., "On relativistic wave equations for particles of arbitrary spin in an electromagnetic field", Proc. R. Soc. London, Ser. A, 173 (1939) 211.
RARITA W. and SCHWINGER J., "On a theory of particles with half integral spin", Phys. Rev., 60 (1941) 61.
FRADKIN E. S., "On the theory of particles with higher spins. (In Russian)", JETP, 20 (1950) 27;
MOLDAUER P. A. and CASE K. M., "Properties of Half-Integral Spin DiracFierz-Pauli Particles", Phys. Rev., 102 (1956) 279;
FRONSDAL C., "On the theory of higher spin fields", Nuovo Cimento Suppl., 9 (1958) 416.
CHANG S. J., "Lagrange Formulation for Systems with Higher Spin", Phys. Rev., 161 (1967) 1308.
SINGH L. P. S. and HAGEN C. R., "Lagrangian formulation for arbitrary spin. 1. The boson case", Phys. Rev. D, 9 (1974) 898.
SINGH L. P. S and HAGEN C. R., "Lagrangian formulation for arbitrary spin. 2. The Sermion case", Phys. Rev. D, 9 (1974) 910.
FRONSDAL C., "Massless Fields With Integer Spin", Phys. Rev. D, 18 (1978) 3624.
FANG J. and FRONSDAL C., "Massless Fields With Half Integral Spin", Phys. Rev. D, 18 (1978) 3630.
CURTRIGHT T., "Massless Field Supermultiplets With Arbitrary Spin", Phys. Lett. B, 85 (1979) 219.
DE WIT B. and FREEDMAN D. Z., "Systematics Of Higher Spin Gauge Fields", Phys. Rev. D, 21 (1980) 358.
VASILIEV M. A., " 'Gauge' Form Of Description Of Massless Fields With Arbitrary Spin" (in Russian), Yad. Fiz., 32 (1980) 855
(Sov. J. Nucl. Phys., 32 (1980) 439);
"Free Massless Fermionic Fields Of Arbitrary Spin In D-Dimensional De Sitter Space", Nucl. Phys. B, 301 (1988) 26;
LOPATIN V. E. and VASILIEV M. A., "Free Massless Bosonic Fields Of Arbitrary Spin In d-Dimensional De Sitter Space", Mod. Phys. Lett. A, 3 (1988) 257.
MACDOWELL S. W. and MANSOURI F., "Unified Geometric Theory Of Gravity And Supergravity", Phys. Rev. Lett, 38 (1977) 739, 1376(E).
KALUZA T., "Zum Unitätsproblem in der Physik", Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) (1921) 966;
KLEIN O., "Quantentheorie und fünfdimensionale Relativitätstheorie", Z. Phys., 37 (1926) 895
(Surveys High Energ. Phys., 5 (1986) 241);
EINSTEIN A. and BERGMANN P., "On A Generalization Of Kaluza's Theory Of Electricity", Ann. Math, 39 (1938) 683.
CURTRIGHT T. L. and FREUND P. G. O., "Massive Dual Fields", Nucl. Phys. B, 172 (1980) 413;
DELBOURGO R. and JARVIS P. D., "Exotic Gauge Potential Representations And Ghost Counting Via Orthosymplectic Brs Supersymmetry", J. Phys. A, 16 (1983) L275;
CURTRIGHT T., "Generalized Gauge Fields", Phys. Lett. B, 165 (1985) 304.
AULAKH C. S., KOH I. G. and OUVRY S., "Higher Spin Fields With Mixed Symmetry", Phys. Lett. B, 173 (1986) 284;
LABASTIDA J. M. F. and MORRIS T. R., "Massless Mixed Symmetry Bosonic Free Fields", Phys. Lett. B, 180 (1986) 101;
CHUNG K. S., HAN C. W., KIM J. K. and KOH I. G., "Brs Structure And Gauge Invariant Actions For Higher Spin Fields", Phys. Rev. D, 37 (1988) 1079.
OUVRY S. and STER N J., "Gauge Fields Of Any Spin Arid Symmetry", Phys. Lett. B, 177 (1986) 335.
BENGTSSON A. K. H, "A Unified Action For Higher Spin Gauge Bosons From Covariant String Theory", Phys. Lett. B, 182 (1986) 321;
HENNEAUX M. and TEITELBOIM C., in "Quantum Mechanics of Fundamental Systems, 2, edited by TEITELBOIM C. and ZANELLI J. (Plenum Press, New York) 1988, p. 113.
SIEGEL W. and ZWIEBACH B., "Gauge String Fields from the Light Cone", Nucl. Phys. B, 282 (1987) 125;
SIEGEL W., "Gauging Ramond String Fields Via OSP(1,1/2)", Nucl. Phys. B, 284 (1987) 632.
LABASTIDA J. M. F., "Massless Bosonic Free Fields", Phys. Rev. Lett, 58 (1987) 531.
LABASTIDA J. M. F., "Massless Fermionic Free Fields", Phys. Lett. B, 186 (1987) 365.
LABASTIDA J. M. F, "Massless Particles In Arbitrary Representations Of The Lorentz Group", Nucl. Phys. B, 322 (1989) 185.
CAMPOLEONI A., FRANCIA D., MOURAD J. and SAGNOTTI A., "Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields", Nucl. Phys. B, 815 (2009) 289 [arXiv:0810.4350 [hep-th]].
CAMPOLEONI A., FRANCIA D., MOURAD J. and SAGNOTTI A., "Unconstrained Higher Spins of Mixed Symmetry. II. Fermi Fields", to appear in Nucl. Phys. B [arXiv:0904.4447 [hep-th]].
FRANCIA D. and SAGNOTTI A., "On the geometry of higher-spin gauge fields", Class. Quantum Grav., 20 (2003) S473 [arXiv:hep-th/0212185].
SAGNOTTI A. and TSULAIA M., "On higher spins and the tensiohless limit of string theory", Nucl. Phys. B, 682 (2004) 83 [arXiv:hep-th/ 0311257].
SAGNOTTI A., Open Strings And Their Symmetry Groups, in Cargese '87, NonPerturbative Quantum Field Theory edited by MACK G. et al. (Pergamon Press) 1988, p. 521, arXiv:hep-th/0208020;
PRADISI G. and SAGNOTTI A., "Open String Orbifolds", Phys. Lett. B, 216 (1989) 59;
HORAVA P., "Strings On World Sheet Orbifolds", Nucl. Phys. B, 327 (1989) 461;
"Background Duality Of Open String Models", Phys. Lett. B, 231 (1989) 251;
BIANCHI M. and SAGNOTTI A., "On The Systematics Of Open String Theories", Phys. Lett. B, 247 (1990) 515;
"Twist Symmetry And Open String Wilson Lines", Nucl. Phys. B, 361 (1991) 519;
BIANCHI M., PRADISI G. and SAGNOTTI A., "Toroidal compactification and symmetry breaking in open string theories", Nucl. Phys. B, 376 (1992) 365;
SAGNOTTI A., "A Note on the Green-Schwarz mechanism in open string theories", Phys. Lett. B, 294 (1992) 196 [arXiv:hep-th/9210127].
For reviews see: DUDAS E., "Theory and phenomenology of type I strings and M-theory", Class. Quantum Grav., 17 (2000) R41 [arXiv:hep-ph'/0006190];
ANGELANTONJ C. and SAGNOTTI A., "Open strings" Phys. Rep., 371 (2002) 1; 339(E) [arXiv:hep-th/0204089];
BLUMENHAGEN R., KORS B., LUST D. and STIEBERGER S., "Four- dimensional String Compactifications with D-Branes, Orientifolds and Fluxes", Phys. Rep., 445 (2007) 1 [arXiv:hep-th/0610327].
DIXON L. J. and HARVEY J. A., "String Theories In Ten-Dimensions Without SpaceTime Supersymmetry", Nucl. Phys. B, 274 (1986) 93;
SEIBERG N. and WITTEN E., "Spin Structures In String Theory", Nucl. Phys. B, 276 (1986) 272.
GLIOZZI F., SCHERK J. and OLIVE D. L, "Supersymmetry, Supergravity Theories And The Dual Spinor Model", Nucl. Phys. B, 122 (1977) 253.
PASHNEV A. and TSULAIA M., "Dimensional reduction and BRST approach to the description of a Regge trajectory", Mod. Phys. Lett. A, 12 (1997) 861 [arXiv:hepth/9703010],
"Description of the higher massless irreducible integer spins in the BRST approach", Mod. Phys. Lett. A, 13 (1998) 1853 [arXiv:hep-th/9803207];
BURDIK C., PASHNEV A. and TSULAIA M., "The Lagrangian description of representations of the Poincare group", Nucl. Phys. Proc. Suppl, 102 (2001) 285 [arXiv:hep-th/0103143];
BUCHBINDER I. L., PASHNEV A. and TSULAIA M., "Lagrangian formulation of the massless higher integer spin fields in the AdS background", Phys. Lett. B, 523 (2001) 338 [arXiv:hep-th/0109067],
"Massless higher spin fields in the AdS background and BRST constructions for nonlinear algebras", arXiv:hep-th/0206026;
BUCHBINDER I. L., KRYKHTIN V. A. and PASHNEV A., "BRST approach to Lagrangian construction for fermionic massless higher spin fields", Nucl. Phys. B, 711 (2005) 367 [arXiv:hepth/0410215];
BUCHBINDER I. L., KRYKHTIN V. A. and LAVROV P. M., "Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space" Nucl. Phys. B, 762 (2007) 344 [arXiv:hep-th/0608005].
FRANCIA D. and SAGNOTTI A., "Free geometric equations for higher spins", Phys. Lett. B, 543 (2002) 303 [arXiv:hep-th/0207002].
DAMOUR T. and DESER S., "'Geometry' Of Spin 3 Gauge Theories", Ann. Poincaré Phys. Theor., 47 (1987) 277.
FRANCIA D., Ph.D. Thesis, University Roma III (2006).
FRANCIA D., MOURAD J. and SAGNOTTI A., "Current exchanges and unconstrained higher spins", Nucl. Phys. B, 773 (2007) 203 [arXiv:hep-th/0701163].
BEKAERT X. and BOULANGER N., "Tensor gauge fields in arbitrary representations of GL(D,R): Duality and Poincare lemma", Commun. Math. Phys., 245 (2004) 27 [arXiv:hep-th/0208058];
"On geometric equations and duality for free higher spins", Phys. Lett. B, 561 (2003) 183 [arXiv:hep-th/0301243];
"Tensor gauge fields in arbitrary representations of GL(D,R). II: Quadratic actions", Commun. Math. Phys., 271 (2007) 723 [arXiv:hep-th/0606198];
DE MEDEIROS P. and HULL C., "Geometric second order field equations for general tensor gauge fields", JHEP, 0305 (2003) 019 [arXiv:hepth/0303036]
FRANCIA D., "Geometric Lagrangians for massive higher-spin fields", Nucl. Phys. B, 796 (2008) 77 [arXiv:0710.5378 [hep-th]],
"Geometric massive higher spins and current exchanges", Fortschr. Phys., 56 (2008) 800 [arXiv:0804.2857 [hep-th]].
METSAEV R. R., "Massless mixed symmetry bosonic free fields in d-dimensional anti-de Sitter space-time" Phys. Lett. B, 354 (1995) 78;
BURDIK C., PASHNEV A. and TSULAIA M., "On the mixed symmetry irreducible representations of the Poincare group in the BRST approach", Mod. Phys. Lett. A, 16 (2001) 731 [arXiv:hep-th/0101201];
BONELLI G., "On the covariant quantization of tensionless bosonic strings in AdS spacetime", JHEP, 0311 (2003) 028 [arXiv:hep-th/0309222];
BUCHBINDER I. L., KRYKHTIN V. A. and TAKATA H., "Gauge invariant Lagrangian construction for massive higher spin fermionic fields", Phys. Lett. B, 641 (2006) 386 [arXiv:hep-th/0603212];
"Gauge invariant Lagrangian construction for massive bosonic mixed symmetry higher spin fields", Phys. Lett. B, 656 (2007) 253 [arXiv:0707.2181 [hep-th]];
MOSHIN P. Y. and RESHETNYAK A. A., "BRST approach to Lagrangian formulation for mixed-symmetry fermionic higherspin fields", JHEP, 0710 (2007) 040 [arXiv:0707.0386 [hep-th]];
BUCHBINDER I. L., KRYKHTIN V. A. and RYSKINA L. L., "BRST approach to Lagrangian formulation of bosonic totally antisymmeric tensor fields in curved space", Mod. Phys. Lett. A, 24 (2009) 401 [arXiv:0810.3467 [hep-th]];
Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdSd space", arXiv:0902.1471 [hep-th];
ALKALAEV K. B., GRIGORIEV M. and TIPUNIN I. Y., "Massless Poincare modules and gauge invariant equations", arXiv:0811.3999 [hep-th];
ALKALAEV K. B. and GRIGORIEV M., "Unified BRST description of AdS gauge fields", arXiv:0910.2690 [hep-th].
SCHWINGER J., Particles, Sources, and Fields (Addison-Wesley, R-eading, MA, USA) 1970.
FRANCIA D. and SAGNOTTI A., "Minimal local Lagrangians for higher-spin geometry", Phys. Lett. B, 624 (2005) 93 [arXiv:hep-th/0507144].
FRANCIA D. and SAGNOTTI A., "Higher-spin geometry and string theory", J. Phys. Conf. Ser., 33 (2006) 57 [arXiv:hep-th/0601199].
FRANCIA D., MOURAD J. and SAGNOTTI A., "(A)dS exchanges and partially-massless higher spins", Nucl. Phys. B, 804 (2008) 383 [arXiv:0803.3832'[hep-th]].
BUCHBINDER I. L., GALAJINSKY A. V. and KRYKHTIN V. A., "Quartet unconstrained formulation for massless higher spin fields", Nucl. Phys. B, 779 (2007) 155 [arXiv:hepth/0702161].
BRINK L., METSAEV R. R. and VASILIEV M. A., "HOW massless are massless fields in AdS(d)", Nucl. Phys. B, 586 (2000) 183 [arXiv:hep-th/0005136];
ZINOVIEV YU. M., "On massive mixed symmetry tensor fields in Minkowski space and (A)dS" arXiv:hepth/0211233;
"First order formalism for mixed symmetry tensor fields" arXiv:hepth/0304067;
"First order formalism for massive mixed symmetry tensor fields in Minkowski and (A)dS spaces", arXiv:hep-th/0306292;
ALKALAEV K. B., SHAYNKMAN O. V. and VASILIEV M. A., "On the frame-like formulation of mixed-symmetry massless fields in (A)dS(d)", Nucl. Phys. B, 692 (2004) 363 [arXiv:hep-th/0311164];
"Lagrangian formulation for free mixed-symmetry bosonic gauge fields in (A)dS(d)", JHEP, 0508 (2005) 069 [arXiv:hep-th/0501108];
"Frame-like formulation for free mixed-symmetry bosonic massless higher-spin fields in AdS(d)", arXiv:hep-th/0601225;
ALKALAEV K. B, "Two-column higher spin massless fields in AdS(d)", Theor. Math. Phys., 140 (2004) 1253
(Teor. Mat. Fiz., 140 (2004) 424) [arXiv:hep-th/0311212];
ZINOVIEV YU. M, "Frame-like gauge invariant formulation for massive high spin particles", Nucl. Phys. B, 808 (2009) 185 [arXiv:0808.1778 [hep-th]];
"Toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields", Nucl. Phys. B, 812 (2009) 46 [arXiv:0809.3287 [hep-th]];
"Note on antisymmetric spin-tensors", JHEP, 0904 (2009) 035 [arXiv:0903.0262 [hep-th]];
"Frame-like gauge invariant formulation for mixed symmetry fermionic fields", arXiv:0904.0549 [hep-th];
"Towards frame-like gauge invariant formulation for massive mixed symmetry bosonic fields. II. General Young tableau with two rows", arXiv:0907.2140 [hep-th].
SKVORTSOV E. D., "Mixed-Symmetry Massless Fields in Minkowski space Unfolded", JHEP, 0807 (2008) 004 [arXiv:0801.2268 [hep-th]];
"Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space", Nucl. Phys. B, 808 (2009) 569 [arXiv:0807.0903 [hep-th]];
"Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra", arXiv:0904.2919 [hep-th];
BOULANGER N., IAZEOLLA C. and SUNDELL P., "Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism", JHEP, 0907 (2009) 013 [arXiv:0812.3615 [hep-th]];
"Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: II. Oscillator Realization", JHEP, 0907 (2009) 014 [arXiv:0812.4438 [hep-th]];
VASILIEV M. A., "Bosonic conformai higher-spin fields of any symmetry", arXiv:0909.5226 [hep-th].
VASILIEV M. A., "Consistent equation for interacting gauge fields of all spins in (3+1)dimensions", Phys. Lett. B, 243 (1990) 378;
"Properties of equations of motion of interacting gauge fields of all spins in (3+1)-dimensions", Class. Quantum Grav., 8 (1991) 1387;
"More On Equations Of Motion For Interacting Massless Fields Of All Spins In (3+1)-Dimensions", Phys. Lett. B, 285 (1992) 225.
VASILIEV M. A., "Nonlinear equations for symmetric massless higher spin fields in (A)dS(d)", Phys. Lett. B, 567 (2003) 139 [arXiv:hep-th/0304049].
DE MEDEIROS P., "Massive gauge-invariant field theories on spaces of constant curvature", Class. Quantum Grav., 21 (2004) 2571 [arXiv:hep-th/0311254].
MARNELIUS R., "Manifestly Conformai Covariant Description Of Spinning And Charged Particles", Phys. Rev. D, 20 (1979) 2091;
GERSHUN V. D. and TKACH V. I., "Classical And Quantum Dynamics Of Particles With Arbitrary Spin", JETP Lett, 29 (1979) 288
(Pisma Zh. Eksp. Teor. Fiz., 29 (1979) 320);
HOWE P. S., PENATI S., PERNICI M. and TOWNSEND P. K., "Wave Equations For Arbitrary Spin From Quantization Of The Extended Supersymmetric Spinning Particle", Phys. Lett. B, 215 (1988) 555;
"A Particle Mechanics Description Of Antisymmetric Tensor Fields", Class. Quantum Grav., 6 (1989) 1125;
SIEGEL W., "Conformai Invariance Of Extended Spinning Particle Mechanics", Int. J. Mod. Phys. A, 3 (1988) 2713;
MARNELIUS R. and MARTENSSON U., "Derivation Of Manifestly Covariant Quantum Models For Spinning Relativistic Particles", Nucl. Phys. B, 335 (1990) 395;
BANDOS I. A. and LUKIERSKI J., "Tensorial central charges and new superparticle models with fundamental spinor coordinates", Mod. Phys. Lett. A, 14 (1999) 1257 [arXiv:hep-th/9811022];
BANDOS I. A., LUKIERSKI J. and SOROKIN D. P., "Superparticle models with tensorial central charges", Phys. Rev. D, 61 (2000) 045002 [arXiv:hep-th/9904109];
BANDOS I., BEKAERT X., DE AZCARRAGA J. A., SOROKIN D. and TSULAIA M., "Dynamics of higher spin fields and tensorial space", JHEP, 0505 (2005) 031 [arXiv:hep-th/0501113];
BASTIANELLI F., CORRADINI O. and LATINI E., "Higher spin fields from a worldline perspective", JHEP, 0702 (2007) 072 [arXiv:hep-th/0701055],
"Spinning particles and higher spin fields on (A)dS backgrounds", arXiv:0810.0188 [hep-th];
BASTIANELLI F., CORRADINI O. and WALDRON A., "Detours and Paths: BRST Complexes and Worldline Formalism", JHEP, 0905 (2009) 017 [arXiv:0902.0530 [hep-th]];
MARNELIUS R., "Lagrangian higher spin field theories from the O(N) extended supersymmetric particle", arXiv:0906.2084 [hep-th];
CHERNEY D., LATINI E. and WALDRON A., "Generalized Einstein Operator Generating Functions", arXiv:0909.4578 [hep-th].
METSAEV R. R., "Cubic interaction vertices of totally symmetric and mixed symmetry massless representations of the Poincare group in D=6 space-time", Phys. Lett. B, 309 (1993) 39;
"Cubic interaction vertices for massive and massless higher spin fields", Nucl. Phys. B, 759 (2006) 147 [arXiv:hep-th/0512342];
"Cubic interaction vertices for fermionic and bosonic arbitrary spin fields", arXiv:0712.3526 [hep-th].
HORVATHY P. A., PLYUSHCHAY M. S. and VALENZUELA M., "Bosonized supersymmetry from the Majorana-Dirac-Staunton theory and massive higher-spin fields", Phys. Rev. D, 77 (2008) 025017 [arXiv:0710.1394 [hep-th]];
BEKAERT X., DE TRAUBENBERG M. R. and VALENZUELA M., "An infinite supermultiplet of massive higher-spin fields", JHEP, 0905 (2009) 118 [arXiv:0904.2533 [hep-th]].
VELO G. and ZWANZIGER D., "Propagation And Quantization Of Rarita-Schwing er Waves In An External Electromagnetic Potential", Phys. Rev., 186 (1969) 1337;
"Noncausality and other defects of interaction Lagrangians for particles with spin one and higher," Phys. Rev., 188 (1969) 2218;
"Fallacy Of Perturbative Methods For Higher Spin Equations", Lett. Nuovo Cimento, 15 (1976) 39.
ARGYRES P. C. and NAPPI C. R., "Massive Spin-2 Bosonic String States In An Electromagnetic Background", Phys. Lett. B, 224 (1989) 89.
PORRATI M. and RAHMAN R., "Causal Propagation of a Charged Spin 3/2 Field in an External Electromagnetic Background", Phys. Rev. D, 80 (2009) 025009 [arXiv:0906.1432 [hep-th]].
ARAGONE C., "Inconsistency of interaction between the gravitational field and the tensor meson field", Nuovo Cimento A, 64 (1969) 841;
ARAGONE C. and DESER S., "Constraints on gravitationally coupled tensor fields", Nuovo Cimento A, 3 (1971) 709.
WEINBERG, "Photons And Gravitons In S Matrix Theory: Derivation Of Charge Conservation And Equality Of Gravitational And Inertial Mass", Phys. Rev., 135 (1964) 1049.
COLEMAN S. R. and MANDULA J., "All Possible Symmetries Of The S Matrix", Phys. Rev., 159 (1967) 1251.
FREEDMAN D. Z., VAN NlEUWENHUlZEN P. and FERRARA S., "Progress Toward A Theory Of Supergravity", Phys. Rev. D, 13 (1976) 3214;
DESER S. and ZUMINO B., "Consistent Supergravity", Phys. Lett. B, 62 (1976) 335.
ARAGONE C. and DESER S., "Consistency Problems Of Hypergravity", Phys. Lett. B, 86 (1979) 161;
BERENDS F. A., VAN HOLTEN J. W., DE WIT B. and VAN NIEUWENHUIZEN P., "On Spin 5/2 Gauge Fields", J. Phys. A, 13 (1980) 1643.
ARAGONE C. and DESER S., "Consistency Problems Of Spin-2 Gravity Coupling", Nuovo Cimento B, 57 (1980) 33;
ARAGONE C. and LA ROCHE H., "Massless Second Order Tetradic Spin 3 Fields And Higher Helicity Bosons", Nuovo Cimento A, 72 (1982) 149;
DESER S. and YANG Z., "Inconsistency Of Spin 4 - Spin-2 Gauge Field Couplings", Class. Quantum Grav., 7 (1990) 1491.
HAAG R., LOPUSZANSKI J. T. and SOHNIUS M., "All Possible Generators Of Supersymmetries Of The S Matrix", Nucl. Phys. B, 88 (1975) 257.
WEINBERG S. and WITTEN E., "Limits On Massless Particles", Phys. Lett. B, 96 (1980) 59;
BENINCASA P. and CACHAZO F., "Consistency Conditions on the S-Matrix of Massless Particles", arXiv:0705.4305 [hep-th];
PORRATI M. and RAHMAN R., "Intrinsic Cutoff and Acausality for Massive Spin 2 Fields Coupled to Electromagnetism", Nucl. Phys. B, 801 (2008) 174 [arXiv:0801.2581 [hep-th]];
"A Model Independent Ultraviolet Cutoff for Theories with Charged Massive Higher Spin Fields", Nucl. Phys. B, 814 (2009) 370 [arXiv:0812.4254 [hep-th]];
PORRATI M., "Universal Limits on Massless High-Spin Particles", Phys. Rev. D, 78 (2008) 065016 [arXiv:0804.4672 [hep-th]].
BENGTSSON A. K. H., BENGTSSON I. and BRINK L., "Cubic Interaction Terms For Arbitrary Spin", Nucl. Phys. B, 227 (1983) 31;
"Cubic Interaction Terms For Arbitrarily Extended Supermultiplets", Nucl. Phys. B, 227 (1983) 41.
BENGTSSON A. K. H., BENGTSSON I. and LINDEN N., "Interacting Higher Spin Gauge Fields On The Light Front", Class. Quantum Grav., 4 (1987) 1333.
BERENDS F. A., BURGERS G. J. H. and VAN DAM H., "On Spin Three Selfinteractions", Z. Phys. C, 24 (1984) 247.
BERENDS F. A., BURGERS G. J. H. and VAN DAM H., "On The Theoretical Problems In Constructing Interactions Involving Higher Spin Massless Particles", Nucl. Phys. B, 260 (1985) 295.
BERENDS F. A., BURGERS G. J. H. and VAN DAM H., "Explicit Construction Of Conserved Currents For Massless Fields Of Arbitrary Spin", Nucl. Phys. B, 271 (1986) 429.
KOH I. G. and OUVRY S., "Interacting Gauge Fields Of Any Spin And Symmetry", Phys. Lett. B, 179 (1986) 115; 183 (1987) 434(E);
BENGTSSON A. K. H., "BRST Approach To Interacting Higher Spin Gauge Fields", Class. Quantum Grav., 5 (1988) 437.
BENGTSSON A. K. H., Phys. Rev. D, 32 (1985) 2031,
BENGTSSON A. K. H. and BENGTSSON L, "Massless Higher Spin Fields Revisited", Class. Quantum Grav., 3 (1986) 927.
BONELLI G., "On the tensionless limit of bosonic strings, infinite symmetries and higher spins", Nucl. Phys. B, 669 (2003) 159 [arXiv:hep-th/0305155];
BEKAERT X., BOULANGER N. and CNOCKAERT S., "Spin three gauge theory revisited", JHEP, 0601 (2006) 052 [arXiv:hep-th/0508048];
BOULANGER N., LECLERCQ S. and CNOCKAERT S., "Parity violating vertices for spin-3 gauge fields", Phys. Rev. D, 73 (2006) 065019 [arXiv:hep-th/0509118];
BUCHBINDER I. L., FOTOPOULOS A., PETKOU A. C. and TSULAIA M., "Constructing the cubic interaction vertex of higher spin gauge fields", Phys. Rev. D, 74 (2006) 105018 [arXiv:hep-th/0609082];
ZINOVIEV Yu. M., "On massive spin 2 interactions", Nucl Phys. B, 770 (2007) 83 [arXiv:hep-th/0609170];
"On spin 2 electromagnetic interactions", Mod. Phys. Lett. A, 24 (2009) 17 [arXiv:0806.4030 [hep-th]];
"On massive spin 2 electromagnetic interactions", arXiv:0901.3462 [hep-th];
FOTOPOULOS A. and TSULAIA M., "Interacting Higher Spins and the High Energy Limit of the Bosonic String", Phys. Rev. D, 76 (2007) 025014 [arXiv:0705.2939 [hepth]];
FOTOPOULOS A., IHGES N., PETKOU A. C. and TSULAIA M., "Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex", JHEP, 0710 (2007) 021 [arXiv:0708.1399 [hep-th]];
BEKAERT B., JOUNG E. and MOURAD J., "On higher spin interactions with matter", JHEP, 0905 (2009) 126 [arXiv:0903.3338 [hep-th]].
FRADKIN E. S. and VASILIEV M. A., "On the Gravitational Interaction of Massless Higher Spin Fields", Phys. Lett. B, 189 (1987) 89,
"Cubic Interaction in Extended Theories of Massless Higher Spin Fields", Nucl. Phys. B, 291 (1987) 141.
BOULANGER N. and LECLERCQ S., "Consistent couplings between spin-2 and spin3 massless fields", JHEP, 0611 (2006) 034 [arXiv:hep-th/0609221];
ZINOVIEV Yu. M., "On spin S interacting with gravity", Class. Quantum Grav., 26 (2009) 035022 [arXiv:0805.2226 [hep-th]];
BOULANGER N., LECLERCQ S. and SUNDELL P., "On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory", JHEP, 0808 (2008) 056 [arXiv:0805.2764 [hep-th]].
FRADKIN E. S. and VASILIEV M. A., "Candidate To The Role Of Higher Spin Symmetry", Ann. Phys. (NY.), 177 (1987) 63;
VASILIEV M. A., "Free Massless Fields Of Arbitrary Spin In The De Sitter Space And Initial Data For A Higher Spin Superalgebra", Fortschr. Phys., 35 (1987) 741
(Yad. Fiz., 45 (1987) 1784);
"Consistent Equations For Interacting Massless Fields Of All Spins In The First Order In Curvatures", Ann. Phys. (N. Y.), 190 (1989) 59.
SEZGIN E. and SUNDELL P., "On curvature expansion of higher spin gauge theory", Class. Quantum Grav., 18 (2001) 3241 [arXiv:hep-th/0012168];
"Analysis of higher spin field equations in four dimensions", JHEP, 0207 (2002) 055 [arXiv:hep-th/0205132].
SEZGIN E. and SUNDELL P., "An exact solution of 4D higher-spin gauge theory", Nucl. Phys. B, 762 (2007) 1 [arXiv:hep-th/0508158];
IAZEOLLA C., SEZGIN E. and SUNDELL P., "Real Forms of Complex Higher Spin Field Equations and New Exact Solutions", Nucl. Phys. B, 791 (2008) 231 [arXiv:0706.2983 [hep-th]];
DIDENKO D. E. and VASILIEV M. A., "Schwarzschild black hole in 4d higher-spin gauge theory", arXiv:0906.3898 [hep-th].
BEKAERT X., BOULANGER N. and HENNEAUX M., "Consistent deformations of dual formulations of linearized gravity: A no-go result", Phys. Rev. D, 67 (2003) 044010 [arXiv:hep-th/0210278];
BOULANGER N. and CNOCKAERT S., "Consistent deformations of (p,p)-type gauge field theories", JHEP, 0403 (2004) 031 [arXiv:hep-th/0402180];
BEKAERT X., BOULANGER N. and CNOCKAERT S., "NO self-interaction for two-column massless fields", J. Math. Phys., 46 (2005) 012303 [arXiv:hep-th/0407102].
AMATI D., CIAFALONI M. and VENEZIANO G., "Superstring Collisions at Planchan Energies", Phys. Lett. B, 197 (1987) 81;
"Classical and Quantum Gravity Effects from Planckian Energy Superstring Collisions", Int. J. Mod. Phys. A, 3 (1988) 1615;
"Can Space-Time Be Probed Below The String Size?", Phys. Lett. B, 216 (1989) 41;
GROSS D. J. and MENDE P. F., "The High-Energy Behavior of String Scattering Amplitudes", Phys. Lett. B, 197 (1987) 129;
"String Theory Beyond the Planck Scale", Nucl. Phys. B, 303 (1988) 407;
GROSS D. J., "High-Energy Symmetries Of String Theory,", Phys. Rev. Lett, 60 (1988) 1229;
GROSS D. J. and MANES J. L., "The High-Energy Behavior Of Open String Scattering", Nucl. Phys. B, 326 (1989) 73;
MOELLER N. and WEST P. C., "Arbitrary four string scattering at high energy and fixed angle", Nucl. Phys. B, 729 (2005) 1 [arXiv:hep-th/ 0507152].
MALDACENA J. M., "The large N limit of superconformai field theories and supergravity", Adv. Theor. Math. Phys., 2 (1998) 231
(Int. J. Theor. Phys., 38 (1999) 1113) [arXiv:hepth/9711200];
GUBSER S. S., KLEBANOV I. R. and POLYAKOV A. M., "Gauge theory correlators from non-critical string theory", Phys. Lett. B, 428 (1998) 105 [arXiv:hepth/9802109];
WITTEN E., "Anti-de Sitter space and holography", Adv. Theor. Math. Phys., 2 (1998) 253 [arXiv:hep-th/9802150].
SUNDBORG B., "Stringy gravity, interacting tensionless strings and massless higher spins", Nucl. Phys. Proc'Suppl, 102 (2001) 113 [arXiv:hep-th/0103247];
SEZGIN E. and SUNDELL P., "Doubletons and 5D higher spin gauge theory", JHEP, 0109 (2001) 036 [arXiv:hep-th/0105001],
"Massless higher spins and holography", Nucl Phys. B, 644 (2002) 303; 660 (2003) 403(E) [arXiv:hep-th/0205131].
ANSELMI D., "Theory of higher spin tensor currents and central charges", Nucl. Phys. B, 541 (1999) 323 [arXiv:hep-th/9808004].
MlKHAlLOV A., "Notes on higher spin symmetries", arXiv:hep-th/0201019;
KLEBANOV I. R. and POLYAKOV A. M., "AdS dual of the critical O(N) vector model", Phys. Lett. B, 550 (2002) 213 [arXiv:hep-th/0210114];
BIANCHI M., MORALES J. F. and SAMTLEBEN H., "On stringy AdS(5) x S**5 and higher spin holography" JHEP, 0307 (2003) 062 [arXiv:hep-th/0305052];
BEISERT N., BIANCHI M., MORALES J. F. and SAMTLEBEN H., "On the spectrum of AdS/CFT beyond supergravity", JHEP, 0402 (2004) 001 [arXiv:hep-th/0310292],
"Higher spin symmetry and N = 4 SYM", JHEP, 0407 (2004) 058 [arXiv:hep-th/0405057];
BONELLI G., "On the boundary gauge dual of closed tensionless free strings in AdS", JHEP, 0411 (2004) 059 [arXiv:hep-th/0407144];
BIANCHI M., "Higher spins and stringy AdS(5) x S(5)", Fortschr. Phys., 53 (2005) 665 [arXiv:hepth/0409304];
PETKOU A. C., "Holography, duality and higher-spin theories", arXiv:hepth/0410116.
CAMPOLEONI A., "Lagrangian formulations for Bose and Fermi higher-spin fields of mixed symmetry", arXiv:0905.1472 [hep-th].
GOVINDARAJAN T. R., RlNDANI S. D. and SlVAKUMAR M., "Dimensional Reduction And Theories With Massive Gauge Fields", Phys. Rev. D, 32 (1985) 454;
RINDANI S. D. and SlVAKUMAR M., "Gauge-Invariant Description Of Massive Higher-Spin Particles By Dimensional Reduction", Phys. Rev. D, 32 (1985) 3238;
ARAGONE C., DESER S. and YANG Z., "Massive Higher Spin From
RINDANI S. D., SAHDEV D. and SIVAKUMAR M., "Dimensional reduction of symmetric higher spin actions. 1. Bosons", Mod. Phys. Lett. A, 4 (1989) 265;
"Dimensional Reduction Of Symmetric Higher Spin Actions. 2: Fermions", Mod. Phys. Lett. A, 4 (1989) 275.
SIEGEL W., "Hidden Ghosts", Phys. Lett. B, 93 (1980) 170.
M. HAMERMESH, "Group theory and its applications to physical problems" (Dover Publications, New York, NY, USA) 1969;
SCHENSTED I. V., "A course on the application of group theory to Quantum Mechanics" (NEO Press, Peaks Island, ME, USA) 1976;
SAGAN B. E., The symmetric group 2nd edition (Springer-Verlag, New York, NY) 2001.
See also: BEKAERT X and BOULANGER N. "The unitary representations of the Poincare group in any spacetime dimension" arXiv:hep-th/0611263.
KING R. C., "Branching rules for classical Lie groups using tensor and spinor methods", J. Phys. A: Math. Gen., 8 (1975) 429.
SOROKIN D. P. and VASILIEV M. A., "Reducible higher-spin multiplets in flat and AdS spaces and their geometric frame-like formulation", Nucl. Phys. B, 809 (2009) 110 [arXiv:0807.0206 [hep-th]].
DUBOIS-VIOLETTE M. and HENNEAUX M., "Tensor fields of mixed Young symmetry type and N-complexes,", Commun. Math. Phys., 226 (2002) 393 [arXiv:math/0110088];
DE MEDEIROS P. and HULL C., "Exotic tensor gauge theory and duality", Commun. Math. Phys., 235 (2003) 255 [arXiv:hep-th/0208155].