Light Speed Variation with Brane/String-Inspired Space-Time Foam

Recently a series of studies on high energy gamma-ray burst~(GRB) photons suggest a light speed variation with linear energy dependence at the Lorentz violation scale of $3.6 \times 10^{17}~\mathrm{GeV}$, with subluminal propagation of high energy photons in cosmological space. We propose stringy space-time foam as a possible interpretation for this light speed variation. In such a string-inspired scenario, bosonic photon open-string travels \textit{in vacuo} at an infraluminal speed with an energy dependence suppressed by a single power of the string mass scale, due to the foamy structure of space-time at small scales, as described by D-brane objects in string theory. We present a derivation of this deformed propagation speed of the photon field in the infrared (IR) regime. We show that the light speed variation, revealed in the previous studies on GRBs time-delay data, can be well described within such a string approach towards space-time foam. We also derive the value of the effective quantum-gravity mass in this framework, and give a qualitative study on the theory-dependent coefficients. We comment that stringent constraints on Lorentz violation in the photon sector from complementary astrophysical observations can also be explained and understood in the space-time foam context.