Abstract
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.
Highlights
We argued [1, 2, 3] that quantumgravitational effects might cause photons of different energies to propagate at different velocities in vacuo, i.e., that quantum gravity might induce a vacuum refractive index
Our suggestion was based on an analysis of quantum-gravitational fluctuations in the space-time background - ‘space-time foam’ - in a formulation of string theory that used the Liouville field to compensate for departures from the usual description of string vacua based on conformal field theory [4]
We argued [2, 3] that the most sensitive probes of this possibility would be provided by distant astrophysical sources producing energetic photons in short bursts, such as gamma-ray bursters and active galactic nuclei
Summary
We argued [1, 2, 3] that quantumgravitational effects might cause photons of different energies to propagate at different velocities in vacuo, i.e., that quantum gravity might induce a vacuum refractive index. Any model of refraction in spacetime foam that exhibits effects at the level of the MAGIC sensitivity should exhibit three specific properties: (i) photons should exhibit a modified subluminal dispersion relation with Lorentz-violating corrections that grow linearly with E/MQGγ , where MQGγ is close to the Planck scale, (ii) the medium should not refract electrons, so as to avoid the synchrotron-radiation constraints [8], and (iii) the coupling of the photons to the medium must be independent of photon polarization, so as not to have birefringence. The loop effects of virtual electron-positron pairs in a Lorentz-violating background such as a finitetemperature plasma or a space with a boundary do affect the photon dispersion relation These corrections to the velocity of light are all inversely proportional to (powers of) the photon energy, whereas quantum-gravity effects are expected to grow with energy as one approaches the Planck energy [1, 2]. We leave a detailed description for a lengthier paper [26]
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