Abstract
We develop in components the superspace action obtained in [1] describing the first massive level of the open charged superstring in a flat four-dimensional spacetime. In the absence of an electromagnetic background, we show how the Rarita-Schwinger and Fierz-Pauli Lagrangians are retrieved for spin-3/2 and 2, respectively. We then write different forms of the action in the presence of the electromagnetic background. The resulting equations of motion describe the propagation of fields of charged spin-3/2 and spin-1/2 on the one hand, and spin-2, 1 and 0 on the other.
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K. Benakli, N. Berkovits, C.A. Daniel and M. Lize, Higher-spin states of the superstring in an electromagnetic background, JHEP 12 (2021) 112 [arXiv:2110.07623] [INSPIRE].
P.A.M. Dirac, Relativistic wave equations, Proc. Roy. Soc. Lond. A 155 (1936) 447 [arXiv:1936.0111] [INSPIRE].
M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond. A 173 (1939) 211 [arXiv:1939.0140] [INSPIRE].
K. Johnson and E.C.G. Sudarshan, Inconsistency of the local field theory of charged spin 3/2 particles, Annals Phys. 13 (1961) 126 [INSPIRE].
G. Velo and D. Zwanziger, Propagation and quantization of Rarita-Schwinger waves in an external electromagnetic potential, Phys. Rev. 186 (1969) 1337 [INSPIRE].
G. Velo and D. Zwanziger, Noncausality and other defects of interaction lagrangians for particles with spin one and higher, Phys. Rev. 188 (1969) 2218 [INSPIRE].
G. Velo, Anomalous behaviour of a massive spin two charged particle in an external electromagnetic field, Nucl. Phys. B 43 (1972) 389 [INSPIRE].
M. Kobayashi and Y. Takahashi, The Rarita-schwinger Paradoxes, J. Phys. A 20 (1987) 6581 [INSPIRE].
A. Hasumi, R. Endo and T. Kimura, Dirac Quantization of Massive Spin 3/2 Particle Coupled With Magnetic Field, J. Phys. A 12 (1979) L217 [INSPIRE].
W. Cox, On the Lagrangian and Hamiltonian Constraint Algorithms for the Rarita-schwinger Field Coupled to an External Electromagnetic Field, J. Phys. A 22 (1989) 1599 [INSPIRE].
M. Kobayashi and A. Shamaly, Minimal Electromagnetic Coupling for Massive Spin-2 Fields, Phys. Rev. D 17 (1978) 2179 [INSPIRE].
S. Deser, V. Pascalutsa and A. Waldron, Massive spin 3/2 electrodynamics, Phys. Rev. D 62 (2000) 105031 [hep-th/0003011] [INSPIRE].
P. Federbush, Minimal electromagnetic coupling for spin two particles, Nuovo Cim. 19 (1961) 572.
S. Ferrara, M. Porrati and V.L. Telegdi, g = 2 as the natural value of the tree-level gyromagnetic ratio of elementary particles, Phys. Rev. D 46 (1992) 3529 [INSPIRE].
A. Abouelsaood, C.G. Callan Jr., C.R. Nappi and S.A. Yost, Open Strings in Background Gauge Fields, Nucl. Phys. B 280 (1987) 599 [INSPIRE].
C.P. Burgess, Open String Instability in Background Electric Fields, Nucl. Phys. B 294 (1987) 427 [INSPIRE].
V.V. Nesterenko, The Dynamics of Open Strings in a Background Electromagnetic Field, Int. J. Mod. Phys. A 4 (1989) 2627 [INSPIRE].
P.C. Argyres and C.R. Nappi, Massive Spin-2 Bosonic String States in an Electromagnetic Background, Phys. Lett. B 224 (1989) 89 [INSPIRE].
P.C. Argyres and C.R. Nappi, Spin 1 Effective Actions From Open Strings, Nucl. Phys. B 330 (1990) 151 [INSPIRE].
M. Porrati and R. Rahman, Notes on a Cure for Higher-Spin Acausality, Phys. Rev. D 84 (2011) 045013 [arXiv:1103.6027] [INSPIRE].
M. Porrati, R. Rahman and A. Sagnotti, String Theory and The Velo-Zwanziger Problem, Nucl. Phys. B 846 (2011) 250 [arXiv:1011.6411] [INSPIRE].
M. Porrati and R. Rahman, Causal Propagation of a Charged Spin 3/2 Field in an External Electromagnetic Background, Phys. Rev. D 80 (2009) 025009 [arXiv:0906.1432] [INSPIRE].
S. Deser and A. Waldron, Inconsistencies of massive charged gravitating higher spins, Nucl. Phys. B 631 (2002) 369 [hep-th/0112182] [INSPIRE].
N. Berkovits and M.M. Leite, Superspace action for the first massive states of the superstring, Phys. Lett. B 454 (1999) 38 [hep-th/9812153] [INSPIRE].
T. Gregoire, M.D. Schwartz and Y. Shadmi, Massive supergravity and deconstruction, JHEP 07 (2004) 029 [hep-th/0403224] [INSPIRE].
J.M. Martín-García, xAct: Efficient tensor computer algebra for the Wolfram Language, http://xact.es/.
K. Benakli, C.A. Daniel and W. Ke, Open superstring first mass level effective Lagrangian: Massive spin-3/2 fields in an electromagnetic background, Phys. Lett. B 839 (2023) 137788 [arXiv:2211.13691] [INSPIRE].
K. Benakli, C.A. Daniel and W. Ke, Open superstring first mass level effective Lagrangian: Massive spin-2 in an electromagnetic background, Phys. Lett. B 838 (2023) 137680 [arXiv:2211.13689] [INSPIRE].
N. Berkovits, SuperPoincare invariant superstring field theory, Nucl. Phys. B 450 (1995) 90 [hep-th/9503099] [INSPIRE].
N. Berkovits and M.M. Leite, First massive state of the superstring in superspace, Phys. Lett. B 415 (1997) 144 [hep-th/9709148] [INSPIRE].
N. Berkovits, A New description of the superstring, in the proceedings of the 8th Jorge Andre Swieca Summer School: Particles and Fields, (1996), p. 390–418 [hep-th/9604123] [INSPIRE].
T.L. Curtright and P.G.O. Freund, Massive dual fields, Nucl. Phys. B 172 (1980) 413 [INSPIRE].
S. Deser, P.K. Townsend and W. Siegel, Higher Rank Representations of Lower Spin, Nucl. Phys. B 184 (1981) 333 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Nonlinear Electrodynamics from Quantized Strings, Phys. Lett. B 163 (1985) 123 [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press (1992) [ISBN: 978-0-691-02530-8].
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Benakli, K., Daniel, C.A. & Ke, W. Spin-3/2 and spin-2 charged massive states in a constant electromagnetic background. J. High Energ. Phys. 2023, 212 (2023). https://doi.org/10.1007/JHEP03(2023)212
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DOI: https://doi.org/10.1007/JHEP03(2023)212