  It has been suggested that energetic photons propagating in vacuo should
experience a non-trivial refractive index due to the foamy structure of
space-time induced by quantum-gravitational fluctuations. The sensitivity of
recent astrophysical observations, particularly of AGN Mk501 by the MAGIC
Collaboration, approaches the Planck scale for a refractive index depending
linearly on the photon energy. We present here a new derivation of this
quantum-gravitational vacuum refraction index, based on a stringy analogue of
the interaction of a photon with internal degrees of freedom in a conventional
medium. We model the space-time foam as a gas of D-particles in the bulk
space-time of a higher-dimensional cosmology where the observable Universe is a
D3-brane. The interaction of an open string representing a photon with a
D-particle stretches and excites the string, which subsequently decays and
re-emits the photon with a time delay that increases linearly with the photon
energy and is related to stringy uncertainty principles. We relate this
derivation to other descriptions of the quantum-gravitational refractive index
in vacuo.
