Abstract
The Large High Altitude Air Shower Observatory (LHAASO) recently reported the detection of gamma-ray emissions with energies up to 1.1PeV from the Crab Nebula. Using the absence of vacuum Cherenkov effect by inverse-Compton electrons, we improve previous bounds to linear-order Lorentz invariance violation (LV) in the dispersion relations of electrons by 104 times. We show that the LV effect on electrons is severely constrained, compatible with certain type of LV as expected by some models of quantum gravity (QG), such as the string/D-brane inspired space-time foam. We argue that such models are supported by the Crab Nebula constraints from the LHAASO observations, as well as various LV phenomenologies for photons to date.
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