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

TL;DR

The work develops a non-perturbative, Noether-based realization of asymptotic higher-spin symmetries in 4D asymptotically flat spacetimes, unifying YM, GR, and Einstein-Yang-Mills theories on a phase-space framework anchored at null infinity. Central to the construction is a master charge built from time-dependent Carrollian symmetry parameters and a holomorphic Ashtekar-Streubel symplectic potential, yielding a canonical representation of a higher-spin algebroid that closes into algebras or covariant wedges on non-radiative cuts. The algebraic backbone features Lie algebroids and deformations of the Schouten-Nijenhuis/Wedge algebras, including a covariant wedge $ extsf{W}_{eta}$/$ extsf{W}_{oldsymbol{eta}}$ and a time-extended $ extsf{T}$-algebroid that encodes radiation as transitions between non-radiative states, with a dressing map $ extsf{T}^G$ linking wedge and covariant structures. Key results include explicit dual EOMs, a non-perturbative solution scheme for symmetry parameters, renormalized charges that remain finite in the radiation-free limit, and a coherent connection to celestial OPEs and twistorial formalisms, providing a solid classical foundation for a principled understanding of higher-spin symmetries in flat space holography. The framework preserves a consistent algebraic structure across YM, GR, and EYM and clarifies how memory, soft theorems, and corner data encode bulk dynamics in a non-perturbative setting, with potential implications for quantization and S-matrix constraints in gravitational and gauge theories.

Abstract

This thesis deals with the phase space realization of asymptotic higher spin symmetries, in 4d asymptotically flat spacetimes. 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 $s$. 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 $\mathscr{I}$. 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. 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.

Figures (3)

• Figure 1: Penrose compactification for asymptotically flat spacetimes. $(u,r,z,\bar{z})$ are the Bondi coordinates.
• Figure 2: IR triangle Strominger:2017zoo.
• Figure 3: The soft theorem is a factorization property of scattering amplitudes containing at least one massless particle of energy $\omega$, when $\omega\to 0$. The leading soft theorem has the Weinberg pole PhysRev.140.B516 form ${\mathcal{A}}_{n+1}\overset{\omega \to 0}{=}(\frac{1}{\omega}S^{(0)}+\ldots ){\mathcal{A}}_n$. The leading soft factor $S^{(0)}$ only depends on the momenta of the $n$ external particles. A Taylor series in the energy can be extracted to all orders. The '$\ldots$' contain logarithmic, loop and theory dependent corrections. See the rest of the introduction for multiple references.