Towards a supersymmetric w1+8 symmetry in the celestial conformal field theory

The w1+8 symmetry algebra appears in the Einstein-Yang-Mills theory, proposed recently by Strominger. In this paper, we derive the supersymmetric w1+8 symmetry by using the known results on the operator product expansions (OPEs) between the graviton, gravitino, gluon, and gluino in the supersymmetric version of the above theory. We calculate the four additional commutator relations between the soft currents explicitly. In addition, we analyze the works of Odake et al. and Pope et al. and introduce the additional symmetry current that corresponds to the celestial gluino operator. Through this procedure, all seven commutator relations can be connected to the ones associated with the supersymmetric w1+8 algebra with SU(N) symmetry under the restrictions of wedge modes.