Mixed-helicity bracket of celestial symmetries

Abstract: Celestial symmetries of gravity and gauge theory can be enhanced to a $w_{1+\infty}$ algebra and an $S$-algebra respectively, when restricting to a single graviton/gluon helicity sector. Difficulties in combining both sectors in the full theory have been pointed out in the previous literature. In this work, we face this problem from the covariant phase space perspective and analyze in detail the structure of the mixed-helicity bracket of the higher-spin charges for both gravity and Yang--Mills theory. We show that, when restricting one of the two helicities to the wedge sector, a closed algebra can be obtained for all spins in terms of a notion of shadow charge we introduce. Furthermore, when focusing on the lower spin subalgebra sectors, in the case of gravity, we show that a dual mass extension of the BMS algebra can be consistently constructed; in the case of Maxwell theory, inclusion of magnetic charges allows us to recover a non-vanishing expression for the electromagnetic central charge previously obtained through different methods.