Note on higher spins and holographic symmetry algebra

TL;DR

This paper explores the extension of holographic symmetry algebras to include higher spin particles, revealing new subalgebras and verifying their structure through scattering amplitudes, with implications for theories with non-zero cosmological constant.

Contribution

It introduces a higher spin extension of the holographic symmetry algebra, identifying new subalgebras and verifying their structure via explicit amplitude calculations.

Findings

Higher spin particles generate a $w_{}$ subalgebra in the soft symmetry algebra.

The $w_{}$ subalgebra does not commute with the $w_{1+}$ subalgebra from soft gravitons.

The soft algebra for colored higher spin particles is verified using tree-level 4-point MHV amplitudes.

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.