Search for anisotropic Lorentz invariance violation with {\gamma}-rays
While Lorentz invariance, the fundamental symmetry of Einstein's theory of General Relativity, has been tested to a great level of detail, Grand Unified Theories that combine gravity with the other three fundamental forces may result in a violation of Lorentz symmetry at the Planck scale. These energies are unattainable experimentally. However, minute deviations from Lorentz invariance may still be present at much lower energies. These deviations can accumulate over large distances, making astrophysical measurements the most sensitive tests of Lorentz symmetry. One effect of Lorentz invariance violation is an energy dependent photon dispersion of the vacuum resulting in differences of the light travel time from distant objects. The Standard-Model Extension (SME) is an effective theory to describe the low-energy behavior of a more fundamental Grand Unified Theory, including Lorentz and CPT violating terms. In the SME the Lorentz violating operators can in part be classified by their mass-dimension d, with the lowest order being d=5. However, measurements of photon polarization have constrained operators with d=5 setting lower limits on the energy at which they become dominant well beyond the Planck scale. On the other hand, these operators also violate CPT, and thus d=6 could be the leading order. In this paper we present constraints on all 25 real coefficients describing anisotropic non-birefringent Lorentz invariance violation at mass dimension d=6 in the SME. We used Fermi-LAT observations of 25 active galactic nuclei to constrain photon dispersion and combined our results with previously published limits in order to simultaneously constrain all 25 coefficients. This represents the first set of constraints on these coefficients of a mass-dimension d=6, whereas previous measurements were only able to constrain linear combinations of all 25 coefficients.