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

TL;DR

This paper extends the celestial CFT approach to construct the asymptotic symmetry algebra of maximally supersymmetric $ ext{N}=8$ supergravity in four-dimensional flat spacetime, revealing the structure of its extended symmetries.

Contribution

It constructs the $ ext{N}=8$ supergravity asymptotic symmetry algebra using celestial CFT, including super-Poincaré and R-symmetry currents, and clarifies the absence of infinite-dimensional R-symmetry extension.

Findings

Constructed $ ext{N}=8$ supergravity asymptotic symmetry algebra $ ext{$ $}$sbms$_4$.

Identified super-Poincaré and $ ext{SU}(8)_R$ current algebras on the celestial sphere.

Showed no infinite-dimensional extension of the global $ ext{SU}(8)_R$ algebra.

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-Poincar\'{e} 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.