Symmetries of the Celestial Supersphere

We study the celestial CFT dual to theories with bulk supersymmetry. The boundary theory realizes supersymmetry in the spirit of the Green-Schwarz superstring: there is manifest 4d super-Poincaré symmetry, but no 2d superconformal symmetry. Nevertheless, we can extend the celestial sphere itself to a supermanifold – the celestial supersphere. This provides a unified framework for describing key features of celestial holography, including conformally soft theorems, OPEs, and chiral soft algebras. Using these tools, we demonstrate that the ${\mathfrak{b}\mathfrak{m}\mathfrak{s}}_4$ algebra extends to a novel ${\mathfrak{s}\mathfrak{b}\mathfrak{m}\mathfrak{s}}_{4\mathrm{\mid }\mathcal{N}}$ algebra. We also relate the supersymmetric $L(w_{1+\mathrm{\infty }}^{\wedge })$ algebra to Hamiltonian vector fields on ${\mathbb{C}}^{2\mathrm{\mid }\mathcal{N}}$, consistent with the expectation from twistor theory, and deduce the deformation of this algebra by a cosmological constant, $\mathrm{\Lambda }$. These results are all universal and independent of the specific details of the underlying theory.