Multi-Particle Contributions to the Celestial Algebra in the ${\cal N}=8$ Supergravity

Recently, Calkins and Pate calculated the multi-particle operator product expansions (OPEs) of single-particle celestial operators with two-particle celestial operators in pure Einstein gravity. We apply their construction to the graviton, gravitinos, graviphotons, graviphotinos and scalars in ${\cal N}=8$ supergravity. By performing various contour integrals on these multi-particle OPEs, we obtain ninety-five (anti)commutators for the single-particle contributions from the celestial soft current algebra (derived from the single-particle OPEs) in a two-dimensional boundary. Moreover, these ninety-five multi-particle OPEs provide nontrivial relations between the corresponding celestial amplitudes. The triple-collinear limits between these bosonic and fermionic particles from the four-dimensional bulk are also described as a double check. Finally, we implicitly propose both the multi-particle OPEs of single-particle celestial operators with $(N-1)$-particle celestial operators and the corresponding (anti)commutators for the modes of celestial operators that have linear terms (or single-particle exchange terms due to the sum of $N$-particle factorization channels from amplitudes) on the right-hand sides.