Asymptotic Higher Spin Symmetries: Noether Realization & Algebraic Structure in Einstein-Yang-Mills Theory

Abstract

This thesis deals with the phase space realization of asymptotic higher spin symmetries, in 4-dimensional asymptotically flat spacetimes. These symmetries live on the conformal null boundary, namely null infinity, and were first revealed few years ago via the study of conformally soft gluons and gravitons operator product expansions, in the context of celestial holography. Connections with twistor theory and phase space realization followed soon after. In the gravitational case for instance, these symmetries generalize the BMS algebra to include an infinite tower of symmetry generators constructed from tensors on the sphere of arbitrary high rank s. The bulk interpretation of these transformation parameters is still largely under investigation.

Building on a first series of results on their canonical representation, we develop the necessary framework to define Noether charges for all degrees s. Importantly, we construct these charges out of a `holomorphic' asymptotic symplectic potential, such that we obtain an infinite collection of charges conserved in the absence of radiation. The classical symmetry is then realized non-perturbatively and non-linearly in the so-called holomorphic coupling constant, generalizing the perturbative linear and quadratic approach known so far. The infinitesimal action defines a symmetry algebroid which reduces to a symmetry algebra at non-radiative cuts of null infinity. The key ingredient for our construction is to consider field and time dependent symmetry parameters constrained to evolve according to equations of motion dual to (a truncation of) the asymptotic equations of motion in vacuum. We expose our results for Yang-Mills, General Relativity, and Einstein-Yang-Mills theories.

This canonical analysis comes hand in hand with an in-depth study of the algebraic structure underlying the symmetry. We reveal several Lie algebroid and Lie algebra brackets, which connect the Carrollian, celestial and twistorial realizations. We show that these brackets are a deformation of the soft celestial algebra, where the deformation parameters are the radiative asymptotic data. On the one hand they allow us to define the symmetry algebra at non-radiative cuts of null infinity, for arbitrary values of the asymptotic shear and gauge potential. On the other hand, we can accommodate for radiation using the algebroid framework.

For the specific case of non-abelian gauge theory, we also investigate how the asymptotic expansion around null infinity of the full Yang-Mills equations of motion in vacuum can be recast in terms of the higher spin charge aspects. Since the analysis of higher spin symmetries is for now inherent to a truncation of the latter equations of motion, this paves the way towards the understanding of the relevance of these symmetries in the full theory.