Note on higher spins and holographic symmetry algebra

A bstract 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 ∞ which is generated by the conformally soft higher-spin particles . This w ∞ subalgebra does not commute with the w 1+∞ subalgebra 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.