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The $w_{1+\infty}$ symmetry algebra appears in the Einstein--Yang--Millstheory, proposed recently by Strominger. In this paper, we derive thesupersymmetric $w_{1+\infty}$ symmetry by using the known results on theoperator product expansions (OPEs) between the graviton, gravitino, gluon, andgluino in the supersymmetric version of the above theory. We calculate the fouradditional commutator relations between the soft currents explicitly. Inaddition, we analyze the works of Odake et al. and Pope et al. and introducethe additional symmetry current that corresponds to the celestial gluinooperator. Through this procedure, all seven commutator relations can beconnected to the ones associated with the supersymmetric $w_{1+\infty}$ algebrawith $SU(N)$ symmetry under the restrictions of wedge modes.

Toward A Supersymmetric $w_{1+\infty}$ Symmetry in the Celestial Conformal Field Theory