Celestial $s{w}_{1+\mathrm{\infty }}$ algebra in Einstein-Yang-Mills theory

From a study of the subleading structure of the asymptotic equations of motion in Einstein-Yang-Mills theory, we construct charges that are conserved up to quadratic order in non-radiative vacuum. We then show that these higher spin charges obey the celestial $s{w}_{1+\mathrm{\infty }}$ symmetry algebra found earlier from the OPE of positive-helicity conformally soft gluons and gravitons.