Carrollian $\mathscr{L}w_{1+\infty}$ representation from twistor space
Résumé
We construct an explicit realization of the action of the $\mathscr{L}w_{1+\infty}$ loop algebra on fields at null infinity. This action is directly derived by Penrose transform of the geometrical action of $\mathscr{L}w_{1+\infty}$ 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 $\mathscr{L}w_{1+\infty}$ Noether charges on the asymptotic phase space.
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