New constraints on Planck-scale Lorentz violation in QED from the Crab Nebula

We set constraints on O( E / M ) Lorentz violation in QED in an effective field theory framework. A major consequence of such assumptions is the modification of the dispersion relations for electrons/positrons and photons, which in turn can affect the electromagnetic output of astrophysical objects. We compare the information provided by multiwavelength observations with a full and self-consistent computation of the broad-band spectrum of the Crab Nebula. We cast constraints of the order of 10 −5 at 95% confidence level on the lepton Lorentz violation parameters.