Carrollian $\mathscr Lw_{1+\infty}$ representation from twistor space

Abstract

We construct an explicit realization of the action of the \mathscr Lw_{1+∞}ℒw1+∞ loop algebra on fields at null infinity. This action is directly derived by Penrose transform of the geometrical action of \mathscr Lw_{1+∞}ℒw1+∞ symmetries in twistor space, ensuring that it forms a representation of the algebra. Finally, we show that this action coincides with the canonical action of \mathscr Lw_{1+∞}ℒw1+∞ Noether charges on the asymptotic phase space.