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.
