Asymptotic Higher Spin Symmetries I: Covariant Wedge Algebra in Gravity

Abstract

In this paper, we study gravitational symmetry algebras that live on 2-dimensional cuts $S$ of asymptotic infinity. We define a notion of wedge algebra $\mathcal{W}(S)$ which depends on the topology of $S$. For the cylinder $S={\mathbb{C}}^{\ast }$ we recover the celebrated $L{w}_{1+\infty }$ algebra. For the 2-sphere $S^2$, the wedge algebra reduces to a central extension of the anti-self-dual projection of the Poincaré algebra. We then extend $\mathcal{W}(S)$ outside of the wedge space and build a new Lie algebra ${\mathcal{W}}_{\sigma }(S)$, which can be viewed as a deformation of the wedge algebra by a spin two field $\sigma$ playing the role of the shear at a cut of $\mathcal{I}$. This algebra represents the gravitational symmetry algebra in the presence of a non trivial shear and is characterized by a covariantized version of the wedge condition. Finally, we construct a dressing map that provides a Lie algebra isomorphism between the covariant and regular wedge algebras.

40 pages. v2: typos corrected. Ref added. Published in LMP. v3: typos corrected + 1 paragraph added in the intro and 1 in section 4.2

References in corpus (6)

• Asymptotic symmetries and subleading soft graviton theorem
• The Weyl BMS group and Einstein's equations
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space

Cited by in corpus (3)

• Multiparticle Contributions to the Celestial OPE
• Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity
• Asymptotic Higher Spin Symmetries IV: Einstein-Yang-Mills Theory