Asymptotic Symmetry algebra of $\mathcal{N}=8$ Supergravity

Abstract

The asymptotic symmetry algebra of $\mathcal{N}=1$ supergravity was recently constructed using the well-known $2$D celestial CFT (CCFT) technique in ArXiv: 2007.03785. In this paper, we extend the construction to the maximally supersymmetric four dimensional $\mathcal{N}=8$ supergravity theory in asymptotically flat spacetime and construct the extended asymptotic symmetry algebra, which we call $\mathcal{N}=8$ ${\mathfrak{sbms}}_4$. We use the celestial CFT technique to find the appropriate currents for extensions of $\mathcal{N}=8$ super-Poincaré and $\mathrm{SU}(8{)}_R$ R-symmetry current algebra on the celestial sphere ${\mathcal{CS}}^2$. We generalise the definition of shadow transformations and show that there is \textit{no} infinite dimensional extension of the global $\mathrm{SU}(8{)}_R$ algebra in the theory.

arXiv comment39 pages