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Lorentz invariance plays a fundamental role in modern physics. However, tinyviolations of the Lorentz invariance may arise in some candidate quantumgravity theories. Prominent signatures of the gravitational Lorentz invarianceviolation (gLIV) include anisotropy, dispersion, and birefringence in thedispersion relation of gravitational waves (GWs). Using a total of 50 GW eventsin the GW transient catalogs GWTC-1 and GWTC-2, we perform an analysis on theanisotropic birefringence phenomenon. The use of multiple events allows us tocompletely break the degeneracy among gLIV coefficients and globally constrainthe coefficient space. Compared to previous results at mass dimensions 5 and 6for the Lorentz-violating operators, we tighten the global limits of 34coefficients by factors ranging from $2$ to $7$.

New limits on the Lorentz/CPT symmetry through fifty gravitational-wave events