Multiparticle extension of the higher-spin algebra

Abstract

Multiparticle extension of a higher-spin algebra $l$ is introduced as the Lie superalgebra associated with the universal enveloping algebra $U(l)$. While conventional higher-spin symmetry does not mix $n$-particle states with different $n$, multiparticle symmetries do so. Quotients of multiparticle algebras are considered, that act on the space of $n$-particle states with $0\leq n\leq k$ analogous to the space of first $k$ Regge trajectories of String Theory. Original higher-spin algebra is reproduced at $k=1$. Full multiparticle algebras are conjectured to describe vacuum symmetries of string-like extensions of higher-spin gauge theories. Relation of the multiparticle algebras with 3d current operator algebras is described. The central charge parameter, to be related to the parameter ${\mathcal N}$ in $AdS/CFT$ correspondence, enters via the definition of supertrace. Extension to higher $p$-brane-like symmetries is introduced inductively.