GRBs Neutrinos as a Tool to Explore Quantum Gravity induced Lorentz Violation

Lorentz Invariance Violation (LIV) arises in various quantum-gravity theories. As the typical energy for quantum gravity is the Planck mass, $M_{pl}$, LIV will, most likely, be manifested at very high energies that are not accessible on Earth in the foreseeable future. One has to turn to astronomical observations. Time of flight measurement from different astronomical sources set current limits on the energy scale of possible LIV to $> 0.01 M_{pl}$ (for n=1 models) and $> 10^{-9} M_{pl}$ (for n=2). According to current models Gamma-Ray Bursts (GRBs) are accompanied by bursts of high energy ($\gsim 100$TeV) neutrinos. At this energy range the background level of currently constructed neutrino detectors is so low that a detection of a single neutrino from the direction of a GRB months or even years after the burst would imply an association of the neutrino with the burst and will establish a measurement of a time of flight delay. Such time of flight measurements provide the best way to observe (or set limits) on LIV. Detection of a single GRB neutrino would open a new window on LIV and would improve current limits by many orders of magnitude.