A Celestial Soft Symmetry Algebra in the ${\cal N}=8$ Supergravity

Abstract: From the classical $SO({\cal N}=8)$ extended superconformal algebra between the lowest ${\cal N}=8$ multiplet in two dimensions obtained by Ademollo et al. (1976), we generalize it for the arbitrary ${\cal N}=8$ multiplet with manifest $SU(8)$ symmetry containing the bosonic $w_{1+\infty}$ algebra. By modifying this ${\cal N}=8$ supersymmetric $w_{1+\infty}$ algebra, we show that the celestial soft current algebra between the graviton, the gravitinos, the graviphotons, the graviphotinos, and the scalars in two dimensions appears in the ${\cal N}=8$ supergravity theory with $SO(8)$ (or $SU(8)$) global symmetry in four dimensions initiated by de Wit and Freedman (at Stony Brook in 1977). The twenty five couplings in this celestial algebra can be written in terms of eight arbitrary couplings via the Jacobi identity.