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

We determine the N=4 N = 4 supersymmetric W1+∞2,2[λ =1/4] W 1 + ∞ 2 , 2 [ λ = 1 4 ] algebra which is an extension of N=4 N = 4 SO (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 N = 4 supersymmetric w1+∞2,2[λ =1/4] w 1 + ∞ 2 , 2 [ λ = 1 4 ] algebra, in two dimensions with the N=4 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 N = 4 supersymmetric soft current algebra provide the soft current algebras for the N=2,3 N = 2 , 3 supergravity theories, the N=2 N = 2 supergravity coupled to its Abelian vector multiplet and the N=1 N = 1 supersymmetric Maxwell Einstein theory. For the N=2 N = 2 supergravity theory, the soft current algebra can be also realized from the N=2 N = 2 supersymmetric w1+∞K,K[λ =0] w 1 + ∞ K , K [ λ = 0 ] algebra.