Abstract
We study large families of theories of interacting spin 2 particles from the point of view of causality. Although it is often stated that there is a unique Lorentz invariant effective theory of massless spin 2, namely general relativity, other theories that utilize higher derivative interactions do in fact exist. These theories are distinct from general relativity, as they permit any number of species of spin 2 particles, are described by a much larger set of parameters, and are not constrained to satisfy the equivalence principle. We consider the leading spin 2 couplings to scalars, fermions, and vectors, and systematically study signal propagation in all these other families of theories. We find that most interactions directly lead to superluminal propagation of either a spin 2 particle or a matter particle, and interactions that are subluminal generate other interactions that are superluminal. Hence, such theories of interacting multiple spin 2 species have superluminality, and by extension, acausality. This is radically different to the special case of general relativity with a single species of minimally coupled spin 2, which leads to subluminal propagation from sources satisfying the null energy condition. This pathology persists even if the spin 2 field is massive. We compare these findings to the analogous case of spin 1 theories, where higher derivative interactions can be causal. This makes the spin 2 case very special, and suggests that multiple species of spin 2 is forbidden, leading us to general relativity as essentially the unique internally consistent effective theory of spin 2.
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References
M.P. Hertzberg, Gravitation, causality and quantum consistency, arXiv:1610.03065 [INSPIRE].
R.M. Wald, Spin-2 fields and general covariance, Phys. Rev. D 33 (1986) 3613 [INSPIRE].
D. Bai and Y.-H. Xing, Special gravity as alternatives for interacting massless gravitons, arXiv:1610.00241 [INSPIRE].
D. Bai and Y.-H. Xing, On the uniqueness of ghost-free special gravity, arXiv:1702.05756 [INSPIRE].
N. Boulanger, T. Damour, L. Gualtieri and M. Henneaux, Inconsistency of interacting, multigraviton theories, Nucl. Phys. B 597 (2001) 127 [hep-th/0007220] [INSPIRE].
P. Benincasa and F. Cachazo, Consistency conditions on the S-matrix of massless particles, arXiv:0705.4305 [INSPIRE].
S. Deser, Selfinteraction and gauge invariance, Gen. Rel. Grav. 1 (1970) 9 [gr-qc/0411023] [INSPIRE].
C. Deffayet, X. Gao, D.A. Steer and G. Zahariade, From k-essence to generalised Galileons, Phys. Rev. D 84 (2011) 064039 [arXiv:1103.3260] [INSPIRE].
S. Ohashi, N. Tanahashi, T. Kobayashi and M. Yamaguchi, The most general second-order field equations of bi-scalar-tensor theory in four dimensions, JHEP 07 (2015) 008 [arXiv:1505.06029] [INSPIRE].
Y. Ohkuwa, Effect of a background gravitational field on the velocity of neutrinos, Prog. Theor. Phys. 65 (1981) 1058 [INSPIRE].
I.T. Drummond and S.J. Hathrell, QED vacuum polarization in a background gravitational field and its effect on the velocity of photons, Phys. Rev. D 22 (1980) 343 [INSPIRE].
G.M. Shore, Quantum gravitational optics, Contemp. Phys. 44 (2003) 503 [gr-qc/0304059] [INSPIRE].
F.A.E. Pirani, Noncausal behavior of classical tachyons, Phys. Rev. D 1 (1970) 3224 [INSPIRE].
T.J. Hollowood and G.M. Shore, Causality violation, gravitational shockwaves and UV completion, JHEP 03 (2016) 129 [arXiv:1512.04952] [INSPIRE].
G. Goon and K. Hinterbichler, Superluminality, black holes and EFT, JHEP 02 (2017) 134 [arXiv:1609.00723] [INSPIRE].
Y. Choquet-Bruhat, The Cauchy problem for stringy gravity, J. Math. Phys. 29 (1988) 1891 [INSPIRE].
K. Izumi, Causal structures in Gauss-Bonnet gravity, Phys. Rev. D 90 (2014) 044037 [arXiv:1406.0677] [INSPIRE].
H. Reall, N. Tanahashi and B. Way, Causality and hyperbolicity of Lovelock theories, Class. Quant. Grav. 31 (2014) 205005 [arXiv:1406.3379] [INSPIRE].
B.A. Campbell, M.J. Duncan, N. Kaloper and K.A. Olive, Gravitational dynamics with Lorentz Chern-Simons terms, Nucl. Phys. B 351 (1991) 778 [INSPIRE].
R. Jackiw and S.Y. Pi, Chern-Simons modification of general relativity, Phys. Rev. D 68 (2003) 104012 [gr-qc/0308071] [INSPIRE].
S. Dyda, E.E. Flanagan and M. Kamionkowski, Vacuum instability in Chern-Simons gravity, Phys. Rev. D 86 (2012) 124031 [arXiv:1208.4871] [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality constraints on corrections to the graviton three-point coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
A. Gruzinov and M. Kleban, Causality constrains higher curvature corrections to gravity, Class. Quant. Grav. 24 (2007) 3521 [hep-th/0612015] [INSPIRE].
B. Bellazzini, C. Cheung and G.N. Remmen, Quantum gravity constraints from unitarity and analyticity, Phys. Rev. D 93 (2016) 064076 [arXiv:1509.00851] [INSPIRE].
M. Visser, B. Bassett and S. Liberati, Superluminal censorship, Nucl. Phys. Proc. Suppl. 88 (2000) 267 [gr-qc/9810026] [INSPIRE].
F.J. Tipler, Singularities and causality violation, Annals Phys. 108 (1977) 1 [INSPIRE].
K.D. Olum, Superluminal travel requires negative energies, Phys. Rev. Lett. 81 (1998) 3567 [gr-qc/9805003] [INSPIRE].
L.H. Ford and T.A. Roman, Averaged energy conditions and quantum inequalities, Phys. Rev. D 51 (1995) 4277 [gr-qc/9410043] [INSPIRE].
M.S. Morris, K.S. Thorne and U. Yurtsever, Wormholes, time machines and the weak energy condition, Phys. Rev. Lett. 61 (1988) 1446 [INSPIRE].
R. Penrose, A remarkable property of plane waves in general relativity, Rev. Mod. Phys. 37 (1965) 215 [INSPIRE].
G.M. Shore, Constructing time machines, Int. J. Mod. Phys. A 18 (2003) 4169 [gr-qc/0210048] [INSPIRE].
S.M. Carroll, G.B. Field and R. Jackiw, Limits on a Lorentz and parity violating modification of electrodynamics, Phys. Rev. D 41 (1990) 1231 [INSPIRE].
M. Nowakowski, E.A. Paschos and J.M. Rodriguez, All electromagnetic form-factors, Eur. J. Phys. 26 (2005) 545 [physics/0402058] [INSPIRE].
C. Giunti and A. Studenikin, Neutrino electromagnetic properties, Phys. Atom. Nucl. 72 (2009) 2089 [arXiv:0812.3646] [INSPIRE].
C. Broggini, C. Giunti and A. Studenikin, Electromagnetic properties of neutrinos, Adv. High Energy Phys. 2012 (2012) 459526 [arXiv:1207.3980] [INSPIRE].
C. Giunti, K.A. Kouzakov, Y.-F. Li, A.V. Lokhov, A.I. Studenikin and S. Zhou, Electromagnetic neutrinos in laboratory experiments and astrophysics, Annalen Phys. 528 (2016) 198 [arXiv:1506.05387] [INSPIRE].
G. Velo and D. Zwanziger, Propagation and quantization of Rarita-Schwinger waves in an external electromagnetic potential, Phys. Rev. 186 (1969) 1337 [INSPIRE].
J.A. Madore, The characteristic surface of a classical spin-3/2 field in an Einstein-Maxwell background, Phys. Lett. B 55 (1975) 217 [INSPIRE].
J. Madore and W. Tait, Propagation of shock waves in interacting higher spin wave equations, Commun. Math. Phys. 30 (1973) 201.
S. Deser and A. Waldron, Inconsistencies of massive charged gravitating higher spins, Nucl. Phys. B 631 (2002) 369 [hep-th/0112182] [INSPIRE].
R. Rahman, Helicity-1/2 mode as a probe of interactions of a massive Rarita-Schwinger field, Phys. Rev. D 87 (2013) 065030 [arXiv:1111.3366] [INSPIRE].
S. Deser and A. Waldron, Acausality of massive gravity, Phys. Rev. Lett. 110 (2013) 111101 [arXiv:1212.5835] [INSPIRE].
S. Deser, M. Sandora, A. Waldron and G. Zahariade, Covariant constraints for generic massive gravity and analysis of its characteristics, Phys. Rev. D 90 (2014) 104043 [arXiv:1408.0561] [INSPIRE].
G. D’Amico, G. Gabadadze, L. Hui and D. Pirtskhalava, Quasidilaton: theory and cosmology, Phys. Rev. D 87 (2013) 064037 [arXiv:1206.4253] [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, A periodic table of effective field theories, JHEP 02 (2017) 020 [arXiv:1611.03137] [INSPIRE].
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Hertzberg, M.P., Sandora, M. General relativity from causality. J. High Energ. Phys. 2017, 119 (2017). https://doi.org/10.1007/JHEP09(2017)119
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DOI: https://doi.org/10.1007/JHEP09(2017)119