Note on higher spins and holographic symmetry algebra

TL;DR

The paper investigates how higher-spin fields integrate into celestial holography by constructing a higher-spin soft algebra from conformally soft currents $H^{k,\sigma}$ and showing it yields a $w_{\infty}$ subalgebra that does not commute with the graviton-derived $w_{1+\infty}$ (and an $S$-algebra analog for colored states). It develops a detailed OPE framework, defines a wedge-like higher-spin algebra (the $hsa$) with translations and Lorentz-like generators, and identifies two noncommuting copies of infinite-dimensional algebras arising from gravitons and higher-spin states. The leading celestial OPE in Higher Spin Yang-Mills is computed from a tree-level 4-point MHV amplitude and shown to reproduce the proposed higher-spin symmetry structure, with subleading terms fixed by conformal invariance. The work further extends the analysis to curved backgrounds, deriving a deformed higher-spin symmetry algebra in the presence of a cosmological constant $\Lambda$ and verifying essential consistency via Jacobi identities. Altogether, the results suggest a rich, interacting higher-spin holographic symmetry framework that potentially governs self-dual higher-spin theories and invites further exploration in nonflat geometries.

Abstract

In this paper we discuss a higher spin extension of the holographic symmetry algebra for graviton and gluon. Our primary observation is that in the presence of higher spin particles the soft symmetry algebra has a subalgebra isomorphic to $w_{\infty}$ which is generated by the \textit{conformally soft higher spin particles}. This $w_{\infty}$ subalgebra does not commute with the $w_{1+\infty}$ subalegbra generated by the conformally soft gravitons. The same thing holds for the colored higher spin particles. One gets a subalgebra isomorphic to the $S$-algebra which is generated by the conformally soft colored higher spin particles. We further verify the soft algebra for colored higher spin particles using the (tree-level) $4$-point MHV amplitude of the higher spin Yang-Mills theory constructed in arXiv:2210.07130. At the end we also discuss the higher spin extension of the deformed holographic symmetry algebra for non-zero cosmological constant as constructed in arXiv:2312.00876.