Symmetries of the Celestial Supersphere

TL;DR

This paper explores the supersymmetric extension of celestial holography by introducing the celestial supersphere, revealing new algebraic structures and their deformations related to bulk supersymmetry and twistor theory.

Contribution

It constructs the celestial supersphere framework and extends the BMS algebra to a supersymmetric version, connecting it with twistor theory and cosmological constant deformations.

Findings

Extension of BMS algebra to super-BMS algebra.

Relation of supersymmetric $L(w_{1+ abla}^\ ext{wedge})$ algebra to Hamiltonian vector fields.

Deformation of algebra by cosmological constant \(\Lambda\).

Abstract

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-Poincar\'e 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 $\frak{bms}_{4}$ algebra extends to a novel $\frak{sbms}_{4|\mathcal{N}}$ algebra. We also relate the supersymmetric $L(w_{1+\infty}^\wedge)$ algebra to Hamiltonian vector fields on $\mathbb{C}^{2|\mathcal{N}}$, consistent with the expectation from twistor theory, and deduce the deformation of this algebra by a cosmological constant, $\Lambda$. These results are all universal and independent of the specific details of the underlying theory.