Superluminality, Black Holes and Effective Field Theory

Abstract

Under the assumption that a UV theory does not display superluminal behavior, we ask what constraints on superluminality are satisfied in the effective field theory (EFT). We study two examples of effective theories: quantum electrodynamics (QED) coupled to gravity after the electron is integrated out, and the flat-space galileon. The first is realized in nature, the second is more speculative, but they both exhibit apparent superluminality around non-trivial backgrounds. In the QED case, we attempt, and fail, to find backgrounds for which the superluminal signal advance can be made larger than the putative resolving power of the EFT. In contrast, in the galileon case it is easy to find such backgrounds, indicating that if the UV completion of the galileon is (sub)luminal, quantum corrections must become important at distance scales of order the Vainshtein radius of the background configuration, much larger than the naive EFT strong coupling distance scale. Such corrections would be reminiscent of the non-perturbative Schwarzschild scale quantum effects that are expected to resolve the black hole information problem. Finally, a byproduct of our analysis is a calculation of how perturbative quantum effects alter charged Reissner-Nordstrom black holes.

Figures (15)

• Figure 1: Sketch of the Drummond-Hathrell problem Drummond:1979pp. A photon passes a distance $L$ from a Schwarzschild BH of radius $r_{s}$. If the polarization is pointing radially outwards, as indicated by the red lines, the EFT \ref{['QEDEFTIntro']} gives a superluminal speed.
• Figure 2: Sketch of the Vainshtein mechanism for the cubic galileon \ref{['CubicGalileon']} around the Sun. Far from a source, the cubic galileon generates a potential of Newtonian strength $V\sim V_{N}\sim r_{s}/r$. Below the non-linear distance scale $r_{V}\sim \Lambda^{-1}(M/M_{p})^{1/3}$ screening becomes effective and the fifth force is suppressed by a factor of $(r/r_{V})^{3/2}$.
• Figure 3: Sketch of superluminality induced by the Sun for the cubic galileon. Radially moving perturbations travel with a position dependent speed of sound, indicated by the blue curve. The horizontal axis represents $c_{s}=1$. For the purely cubic galileon, $c_{s}\ge 1$ when $r\lesssim r_{V}$, though $c_{s}\to 1$ at large $r$.
• Figure 4: The QED box diagram generates the two $\mathcal{O}(F^{4})$ EFT operators in \ref{['4DEFT']}. Throughout the paper, photons are represented by blue, wavy lines.
• Figure 5: Triangle diagrams generate the three $\sim RFF$ operators in \ref{['4DEFT']}. Throughout the paper, gravitons will be represented by red, curly lines.