  Quantum gravitational fluctuations of the space-time background, described by
virtual D branes, may induce neutrino oscillations if a tiny violation of the
Lorentz invariance (or a violation of the equivalence principle) is imposed. In
this framework, the oscillation length of massless neutrinos turns out to be
proportional to M/E^2, where E is the neutrino energy and M is the mass scale
characterizing the topological fluctuations in the vacuum. Such a functional
dependence on the energy is the same obtained in the framework of loop quantum
gravity.
