  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.
