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

Abstract We determine the N=4 N = 4 supersymmetric W₁+ ^2, 2 =14 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 =14 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 =0 w 1 + ∞ K, K λ = 0 algebra.