Abstract
The effective actions describing the low-energy dynamics of QFTs involving gravity generically exhibit causality violations. These may take the form of superluminal propagation or Shapiro time advances and allow the construction of “time machines”, i.e. spacetimes admitting closed non-spacelike curves. Here, we discuss critically whether such causality violations may be used as a criterion to identify unphysical effective actions or whether, and how, causality problems may be resolved by embedding the action in a fundamental, UV complete QFT. We study in detail the case of photon scattering in an Aichelburg-Sexl gravitational shockwave background and calculate the phase shifts in QED for all energies, demonstrating their smooth interpolation from the causality-violating effective action values at low-energy to their manifestly causal high-energy limits. At low energies, these phase shifts may be interpreted as backwards-in-time coordinate jumps as the photon encounters the shock wavefront, and we illustrate how the resulting causality problems emerge and are resolved in a two-shockwave time machine scenario. The implications of our results for ultra-high (Planck) energy scattering, in which graviton exchange is modelled by the shockwave background, are highlighted.
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References
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].
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].
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].
P.C. Aichelburg and R.U. Sexl, On the gravitational field of a massless particle, Gen. Rel. Grav. 2 (1971) 303 [INSPIRE].
T.J. Hollowood and G.M. Shore, The Causal Structure of QED in Curved Spacetime: Analyticity and the Refractive Index, JHEP 12 (2008) 091 [arXiv:0806.1019] [INSPIRE].
T.J. Hollowood and G.M. Shore, Causality and Micro-Causality in Curved Spacetime, Phys. Lett. B 655 (2007) 67 [arXiv:0707.2302] [INSPIRE].
T.J. Hollowood and G.M. Shore, The Refractive index of curved spacetime: The Fate of causality in QED, Nucl. Phys. B 795 (2008) 138 [arXiv:0707.2303] [INSPIRE].
T.J. Hollowood, G.M. Shore and R.J. Stanley, The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes, JHEP 08 (2009) 089 [arXiv:0905.0771] [INSPIRE].
T.J. Hollowood and G.M. Shore, The Effect of Gravitational Tidal Forces on Vacuum Polarization: How to Undress a Photon, Phys. Lett. B 691 (2010) 279 [arXiv:1006.0145] [INSPIRE].
T.J. Hollowood and G.M. Shore, The Effect of Gravitational Tidal Forces on Renormalized Quantum Fields, JHEP 02 (2012) 120 [arXiv:1111.3174] [INSPIRE].
M.A. Leontovich, in L.I. Mandelshtam, Lectures in Optics, Relativity and Quantum Mechanics in Russian, Nauka, Moscow U.S.S.R. (1972).
G.M. Shore, Causality and superluminal light, in Time and Matter, Proceedings of the International Colloquium on the Science of Time, Venice Italy (2002), I. Bigi and M. Faessler eds., World Scientific, Singapore (2006), pg. 45 [gr-qc/0302116] [INSPIRE].
G.M. Shore, Superluminality and UV completion, Nucl. Phys. B 778 (2007) 219 [hep-th/0701185] [INSPIRE].
G.M. Shore, Constructing time machines, Int. J. Mod. Phys. A 18 (2003) 4169 [gr-qc/0210048] [INSPIRE].
D.J. Gross and P.F. Mende, The High-Energy Behavior of String Scattering Amplitudes, Phys. Lett. B 197 (1987) 129 [INSPIRE].
D.J. Gross and P.F. Mende, String Theory Beyond the Planck Scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE].
G. ’t Hooft, Graviton Dominance in Ultrahigh-Energy Scattering, Phys. Lett. B 198 (1987) 61 [INSPIRE].
I.J. Muzinich and M. Soldate, High-Energy Unitarity of Gravitation and Strings, Phys. Rev. D 37 (1988) 359 [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Superstring Collisions at Planckian Energies, Phys. Lett. B 197 (1987) 81 [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Classical and Quantum Gravity Effects from Planckian Energy Superstring Collisions, Int. J. Mod. Phys. A 3 (1988) 1615 [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Can Space-Time Be Probed Below the String Size?, Phys. Lett. B 216 (1989) 41 [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Higher Order Gravitational Deflection and Soft Bremsstrahlung in Planckian Energy Superstring Collisions, Nucl. Phys. B 347 (1990) 550 [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Planckian scattering beyond the semiclassical approximation, Phys. Lett. B 289 (1992) 87 [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Effective action and all order gravitational eikonal at Planckian energies, Nucl. Phys. B 403 (1993) 707 [INSPIRE].
G. Veneziano, String-theoretic unitary S-matrix at the threshold of black-hole production, JHEP 11 (2004) 001 [hep-th/0410166] [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Towards an S-matrix description of gravitational collapse, JHEP 02 (2008) 049 [arXiv:0712.1209] [INSPIRE].
S.B. Giddings, D.J. Gross and A. Maharana, Gravitational effects in ultrahigh-energy string scattering, Phys. Rev. D 77 (2008) 046001 [arXiv:0705.1816] [INSPIRE].
T.J. Hollowood and G.M. Shore, Causality, Renormalizability and Ultra-High Energy Gravitational Scattering, to appear.
T.J. Hollowood and G.M. Shore, Superluminal Modes and the Lightcone, to appear.
V. Ferrari, P. Pendenza and G. Veneziano, Beamlike Gravitational Waves and Their Geodesics, Gen. Rel. Grav. 20 (1988) 1185 [INSPIRE].
G. D’Appollonio, P. Vecchia, R. Russo and G. Veneziano, Regge behavior saves String Theory from causality violations, JHEP 05 (2015) 144 [arXiv:1502.01254] [INSPIRE].
G. Papallo and H.S. Reall, Graviton time delay and a speed limit for small black holes in Einstein-Gauss-Bonnet theory, JHEP 11 (2015) 109 [arXiv:1508.05303] [INSPIRE].
P.D. D’Eath and P.N. Payne, Gravitational radiation in high speed black hole collisions. 1. Perturbation treatment of the axisymmetric speed of light collision, Phys. Rev. D 46 (1992) 658 [INSPIRE].
R. Penrose, Any space-time has a plane wave as a limit, in Differential geometry and relativity, Reidel Publishing, Dordrecht The Netherlands (1976), pg. 271.
M. Blau, D. Frank and S. Weiss, Fermi coordinates and Penrose limits, Class. Quant. Grav. 23 (2006) 3993 [hep-th/0603109] [INSPIRE].
D. Boyanovsky and R. Holman, On the Perturbative Stability of Quantum Field Theories in de Sitter Space, JHEP 05 (2011) 047 [arXiv:1103.4648] [INSPIRE].
G.M. Shore, ’Faster than light’ photons in gravitational fields: Causality, anomalies and horizons, Nucl. Phys. B 460 (1996) 379 [gr-qc/9504041] [INSPIRE].
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Hollowood, T.J., Shore, G.M. Causality violation, gravitational shockwaves and UV completion. J. High Energ. Phys. 2016, 129 (2016). https://doi.org/10.1007/JHEP03(2016)129
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DOI: https://doi.org/10.1007/JHEP03(2016)129