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Gravitational waves would attain birefringence during their propagation fromdistant sources to the Earth, when the CPT symmetry is broken. If it wassizeable enough, such birefringence could be measured by the Advanced LIGO,Virgo and KAGRA detector network. In this work, we place constraints on thebirefringence of gravitational waves with the third observing run of thisnetwork, i.e. two catalogues GWTC-2 and GWTC-3. For the dispersion relation$\omega^{2}=k^{2}\pm2\zeta k^{3}$, our analysis shows the up-to-date strictestlimit on the CPT-violating parameter, i.e.\textcolor{black}{{$\zeta=4.07^{+5.91}_{-5.79}\times10^{-17}\mathrm{m}$}}, at$68\%$ confidence level. This limit is stricter by $\sim$5 times than theexisting one {($\sim 2\times10^{-16}$m)} and stands for the first$\sim$10GeV-scale test of the CPT symmetry in gravitational waves. The resultsof Bayes factor strongly disfavor the birefringence scenario of gravitationalwaves.

Search for the birefringence of gravitational waves with the third observing run of Advanced LIGO-Virgo