A supersymmetric w1+∞ symmetry, the extended supergravity and the celestial holography

We determine the N=4 supersymmetric W1+∞2,2[λ=14] algebra which is an extension of N=4SO(4) superconformal algebra with vanishing central charge. We identify the soft current algebra between the graviton, the gravitinos, the vectors, the Majorana fermions, the scalar or the pseudoscalar, from the N=4 supersymmetric w1+∞2,2[λ=14] algebra, in two dimensions with the N=4 supergravity theory with SO(4) global symmetry in four dimensions found by Das (at Stony Brook in 1977), via celestial holography. Furthermore, the truncations of N=4 supersymmetric soft current algebra provide the soft current algebras for the N=2,3 supergravity theories, the N=2 supergravity coupled to its Abelian vector multiplet and the N=1 supersymmetric Maxwell Einstein theory. For the N=2 supergravity theory, the soft current algebra can be also realized from the N=2 supersymmetric w1+∞K,K[λ=0] algebra.