Mixed-helicity bracket of celestial symmetries

TL;DR

This paper investigates the algebraic structure of celestial symmetries involving mixed helicities in gravity and gauge theories, introducing shadow charges and dual mass extensions to unify sectors and recover known charges.

Contribution

It provides a detailed analysis of the mixed-helicity brackets, introduces shadow charges for a closed algebra, and constructs dual mass extensions of BMS and electromagnetic charges.

Findings

A closed algebra is obtained when restricting one helicity to the wedge sector.

A dual mass extension of the BMS algebra is constructed for gravity.

Magnetic charges enable a non-vanishing electromagnetic central charge.

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.