A deformed supersymmetric w_{1+infty } symmetry in the celestial conformal field theory

Abstract

By using the K-free complex bosons and the K-free complex fermions, we construct the mathcal {N},{=},2 supersymmetric W_{infty }^{K,K} algebra which is the matrix generalization of previous {{mathcal {N}}},{=},2 supersymmetric W_{infty } algebra. By twisting this {{mathcal {N}}},{=},2 supersymmetric W_{infty }^{K,K} algebra, we obtain the {{mathcal {N}}},{=},1 supersymmetric W_{infty }^{K} algebra which is the matrix generalization of known {{mathcal {N}}},{=},1 supersymmetric topological W_{infty } algebra. From this two-dimensional symmetry algebra, we propose the operator product expansion (OPE) between the soft graviton and gravitino (as a first example), at nonzero deformation parameter, in the supersymmetric Einstein–Yang–Mills theory explicitly. Other six OPEs between the graviton, gravitino, gluon and gluino can be determined completely. At vanishing deformation parameter, we reproduce the known result of Fotopoulos, Stieberger, Taylor and Zhu on the above OPEs via celestial holography.