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Lagrangian BRST formulation of massive higher-spin fields of
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 327-350 Cet article a éte moissonné depuis la source Math-Net.Ru

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We describe the procedure of dimensional reduction of massless fields in $(d+1)$-dimensional Minkowski space to massive fields in $d$ dimensions in the first-quantized setting. The procedure is compatible with the Lagrangian and in a straightforward way determines the inner product for massive fields. The use of the Howe duality and the BRST technique allows keeping the description concise. We consider both bosonic and fermionic mixed-symmetry fields.
Keywords: BRST, dimensional reduction, Lagrangian, gauge invariance, higher-spin theory. 
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A. A. Chekmenev. Lagrangian BRST formulation of massive higher-spin fields of. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 327-350. http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a6/

[1] C. Aragone, S. Deser, Z. Yang, “Massive higher spin from dimensional reduction of gauge fields”, Ann. Phys., 179:1 (1987), 76–96 | DOI | MR

[2] A. I. Pashnev, “Sostavnaya sistema i teoriya polya svobodnoi traektorii Redzhe”, TMF, 78:3 (1989), 384–391 | DOI

[3] X. Bekaert, I. L. Buchbinder, A. Pashnev, M. Tsulaia, “On higher spin theory: strings, BRST, dimensional reductions”, Class. Quantum Grav., 21:10 (2004), S1457–1464, arXiv: hep-th/0312252 | DOI | MR

[4] E. P. Wigner, “On unitary representations of the inhomogeneous Lorentz group”, Ann. Math., 40:1 (1939), 149–204 | DOI | MR

[5] V. Bargmann, E. P. Wigner, “Group theoretical discussion of relativistic wave equations”, Proc. Nat. Acad. Sci. USA, 34:5 (1948), 211–223 | DOI | MR

[6] X. Bekaert, N. Boulanger, “The unitary representations of the Poincaré group in any spacetime dimension”, SciPost Phys. Lect. Notes, 30 (2021), 1–47, arXiv: hep-th/0611263 | DOI

[7] L. P. S. Singh, C. R. Hagen, “Lagrangian formulation for arbitrary spin. 1. The boson case”, Phys. Rev. D, 9:4 (1974), 898–909 | DOI

[8] L. P. S. Singh, C. R. Hagen, “Lagrangian formulation for arbitrary spin. II. The fermion case”, Phys. Rev. D, 9:4 (1974), 910–920 | DOI

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

[10] J. M. F. Labastida, “Massless bosonic free fields”, Phys. Rev. Lett., 58:6 (1987), 531–534 | DOI | MR

[11] J. M. F. Labastida, “Massless particles in arbitrary representations of the Lorentz group”, Nucl. Phys. B, 322:1 (1989), 185–209 | DOI | MR

[12] X. Bekaert, N. Boulanger, “Tensor gauge fields in arbitrary representations of $GL(D,\mathbb R)$. Duality and Poincaré lemma”, Commun. Math. Phys., 245:1 (2004), 27–67, arXiv: hep-th/0208058 | DOI | MR

[13] K. B. Alkalaev, M. Grigoriev, I. Y. Tipunin, “Massless Poincare modules and gauge invariant equations”, Nucl. Phys. B, 823:3 (2009), 509–545, arXiv: 0811.3999 | DOI | MR

[14] A. K. H. Bengtsson, “A unified action for higher spin gauge bosons from covariant string theory”, Phys. Lett. B, 182:3–4 (1986), 321–325 | DOI | MR

[15] S. Ouvry, J. Stern, “Gauge fields of any spin and symmetry”, Phys. Lett. B, 177:3–4 (1986), 335–340 | DOI | MR

[16] M. Henneaux, C. Teitelboim, “First and second quantized point particles of any spin”, Quantum Mechanics of Fundamental Systems 2 (Centro de Estudios Cientificos de Santiago (CECS), 17–20 December, 1987), eds. C. Teitelboim, J. Zanelli, Springer, Boston, MA, 1989, 113–152 | DOI

[17] A. Sagnotti, M. Tsulaia, “On higher spins and the tensionless limit of string theory”, Nucl. Phys. B, 682:1 (2004), 83–116, arXiv: hep-th/0311257 | DOI | MR

[18] G. Bonelli, “On the tensionless limit of bosonic strings, infinite symmetries and higher spins”, Nucl. Phys. B, 669:1–2 (2003), 159–172, arXiv: hep-th/0305155 | DOI | MR

[19] W. Siegel, “Gauging Ramond string fields via $OSp(1,1/2)$”, Nucl. Phys. B, 284:3–4 (1987), 632–642 | DOI | MR

[20] D. Francia, A. Sagnotti, “On the geometry of higher-spin gauge fields”, Class. Quantum Grav., 20:12 (2003), S473–S485, arXiv: hep-th/0212185 | DOI | MR

[21] A. Reshetnyak, “General Lagrangian formulation for higher spin fields with arbitrary index symmetry. 2. Fermionic fields”, Nucl. Phys. B, 869:3 (2013), 523–597, arXiv: 1211.1273 | DOI | MR

[22] K. Alkalaev, A. Chekmenev, M. Grigoriev, “Unified formulation for helicity and continuous spin fermionic fields”, JHEP, 11 (2018), 050, 24 pp., arXiv: 1808.09385 | DOI | MR

[23] V. E. Lopatin, M. A. Vasiliev, “Free massless bosonic fields of arbitrary spin in $d$-dimensional de Sitter space”, Modern Phys. Lett. A, 3:3 (1988), 257–270 | DOI | MR

[24] I. L. Buchbinder, A. Pashnev, M. Tsulaia, “Lagrangian formulation of the massless higher integer spin fields in the AdS background”, Phys. Lett. B, 523:3–4 (2001), 338–346, arXiv: hep-th/0109067 | DOI | MR

[25] Yu. M. Zinoviev, On massive high spin particles in (A)dS, arXiv: hep-th/0108192

[26] K. B. Alkalaev, O. V. Shaynkman, M. A. Vasiliev, “On the frame-like formulation of mixed-symmetry massless fields in (A)$dS_d$”, Nucl. Phys. B, 692:3 (2004), 363–393, arXiv: hep-th/0311164 | DOI | MR

[27] E. D. Skvortsov, “Frame-like actions for massless mixed-symmetry fields in Minkowski space”, Nucl. Phys. B, 808:3 (2009), 569–591, arXiv: 0807.0903 | DOI | MR

[28] A. Campoleoni, D. Francia, J. Mourad, A. Sagnotti, “Unconstrained higher spins of mixed symmetry. I. Bose fields”, Nucl. Phys. B, 815:3 (2009), 289–367, arXiv: 0810.4350 | DOI | MR

[29] E. D. Skvortsov, “Gauge fields in $(A)dS_d$ and connections of its symmetry algebra”, J. Phys. A, 42:38 (2009), 385401, 30 pp., arXiv: 0904.2919 | DOI | MR

[30] N. Boulanger, C. Iazeolla, P. Sundell, “Unfolding mixed-symmetry fields in AdS and the BMV conjecture: I. General formalism”, JHEP, 07 (2009), 013, 61 pp., arXiv: 0812.3615 | DOI | MR

[31] X. Bekaert, N. Boulanger, D. Francia, “Mixed-symmetry multiplets and higher-spin curvatures”, J. Phys. A: Math. Theor., 48:22 (2015), 225401, 17 pp., arXiv: 1501.02462 | DOI | MR

[32] E. Joung, K. Mkrtchyan, “Weyl action of two-column mixed-symmetry field and its factorization around (A)dS space”, JHEP, 06 (2016), 135, 24 pp., arXiv: 1604.05330 | DOI | MR

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

[34] M. A. Vasiliev, “Free massless fermionic fields of arbitrary spin in $d$-dimensional anti-de Sitter space”, Nucl. Phys. B, 301:1 (1988), 26–68 | DOI | MR

[35] R. R. Metsaev, “Fermionic fields in the $d$-dimensional anti-de Sitter spacetime”, Phys. Lett. B, 419:1–4 (1998), 49–56, arXiv: hep-th/9802097 | DOI | MR

[36] K. B. Alkalaev, “Free fermionic higher spin fields in $AdS_5$”, Phys. Lett. B, 519:1–2 (2001), 121–128, arXiv: hep-th/0107040 | DOI | MR

[37] I. L. Buchbinder, V. A. Krykhtin, A. Pashnev, “BRST approach to Lagrangian construction for fermionic massless higher spin fields”, Nucl. Phys. B, 711:1–2 (2005), 367–391, arXiv: hep-th/0410215 | DOI | MR | Zbl

[38] I. L. Buchbinder, V. A. Krykhtin, A. A. Reshetnyak, “BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space”, Nucl. Phys. B, 787:3 (2007), 211–240, arXiv: hep-th/0703049 | DOI | MR

[39] P. Moshin, A. Reshetnyak, “BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields”, JHEP, 10 (2007), 040, 43 pp., arXiv: 0707.0386 | DOI | MR

[40] E. D. Skvortsov, “Mixed-symmetry massless fields in Minkowski space unfolded”, JHEP, 07 (2008), 004, 59 pp., arXiv: 0801.2268 | DOI | MR

[41] Yu. M. Zinoviev, “Frame-like gauge invariant formulation for mixed symmetry fermionic fields”, Nucl. Phys. B, 821:1–2 (2009), 21–47, arXiv: 0904.0549 | DOI | MR

[42] A. Campoleoni, D. Francia, J. Mourad, A. Sagnotti, “Unconstrained higher spins of mixed symmetry. II. Fermi fields”, Nucl. Phys. B, 828:3 (2010), 405–514, arXiv: 0904.4447 | DOI | MR

[43] E. D. Skvortsov, Yu. M. Zinoviev, “Frame-like actions for massless mixed-symmetry fields in Minkowski space. Fermions”, Nucl. Phys. B, 843:3 (2011), 559–569, arXiv: 1007.4944 | DOI | MR

[44] A. Reshetnyak, Constrained BRST–BFV Lagrangian formulations for higher spin fields in Minkowski spaces, arXiv: 1803.04678

[45] A. A. Reshetnyak, “Constrained BRST–BFV and BRST–BV Lagrangians for half-integer HS fields on $R^{1,d-1}$”, Phys. Part. Nucl., 49:5 (2018), 952–957, arXiv: 1803.05173 | DOI

[46] M. Najafizadeh, “Local action for fermionic unconstrained higher spin gauge fields in AdS and dS spacetimes”, Phys. Rev. D, 98:12 (2018), 125012, 15 pp., arXiv: 1807.01124 | DOI | MR

[47] K. Alkalaev, M. Grigoriev, “Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type”, Nucl. Phys. B, 853:3 (2011), 663–687, arXiv: 1105.6111 | DOI

[48] G. Barnich, M. Grigoriev, “Parent form for higher spin fields on anti-de Sitter space”, JHEP, 08 (2006), 013, 38 pp., arXiv: hep-th/0602166 | DOI

[49] A. A. Chekmenev, Dimensional reduction in first quantized BRST approach for free fields, (neopublikovannaya magisterskaya dissertatsiya, nauchnyi rukovoditel M. A. Grigorev), MFTI, M., 2012

[50] R. R. Metsaev, “BRST–BV approach to cubic interaction vertices for massive and massless higher-spin fields”, Phys. Lett. B, 720:1–3 (2013), 237–243, arXiv: 1205.3131 | DOI

[51] Yu. M. Zinoviev, “Toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields”, Nucl. Phys. B, 812:1 (2009), 46–63, arXiv: 0809.3287 | DOI

[52] R. R. Metsaev, “Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields”, JHEP, 11 (2017), 197, 60 pp., arXiv: 1709.08596 | DOI

[53] D. S. Ponomarev, M. A. Vasiliev, “Frame-like action and unfolded formulation for massive higher-spin fields”, Nucl. Phys. B, 839:3 (2010), 466–498, arXiv: 1001.0062 | DOI

[54] A. Pashnev, M. Tsulaya, “Dimensional reduction and BRST approach to the description of a Regge trajectory”, Modern Phys. Lett. A, 12:12 (1997), 861–870, arXiv: hep-th/9703010 | DOI

[55] I. L. Buchbinder, V. A. Krykhtin, “Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimensions”, Nucl. Phys. B, 727:3 (2005), 537–563, arXiv: hep-th/0505092 | DOI

[56] I. Buchbinder, V. Krykhtin, P. Lavrov, “Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space”, Nucl. Phys. B, 762:3 (2007), 344–376, arXiv: hep-th/0608005 | DOI

[57] I. L. Buchbinder, V. A. Krykhtin, L. L. Ryskina, H. Takata, “Gauge invariant Lagrangian construction for massive higher spin fermionic fields”, Phys. Lett. B, 641:15 (2006), 386–392, arXiv: hep-th/0603212 | DOI

[58] R. Howe, “Transcending classical invariant theory”, J. Amer. Math. Soc., 2:3 (1989), 535–552 | DOI | MR

[59] R. Howe, “Remarks on classical invariant theory”, Trans. Amer. Math. Soc., 313 (1989), 539–570 | DOI

[60] G. Barnich, M. Grigoriev, A. Semikhatov, I. Tipunin, “Parent field theory and unfolding in BRST first-quantized terms”, Commun. Math. Phys., 260 (2005), 147–181, arXiv: hep-th/0406192 | DOI

[61] K. B. Alkalaev, M. Grigoriev, “Unified BRST description of AdS gauge fields”, Nucl. Phys. B, 835:1–2 (2010), 197–220, arXiv: 0910.2690 | DOI

[62] K. B. Alkalaev, M. A. Grigoriev, “Continuous spin fields of mixed-symmetry type”, JHEP, 03 (2018), 030, 25 pp., arXiv: 1712.02317 | DOI

[63] J. M. F. Labastida, “Massless fermionic free fields”, Phys. Lett. B, 186:3–4 (1987), 365–369 | DOI