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 $0\le n\le k$ 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.

39 pages, V2: typos corrected, references, clarifications and a new section on the relation with the current operator algebra are added; V3: clarifications added, typos corrected, the version to be published in CQG

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Cited by in corpus (26)

• Higher Spins & Strings
• String Theory as a Higher Spin Theory
• Operator algebra of free conformal currents via twistors
• Higher-Spin Theory and Space-Time Metamorphoses
• From Higher Spins to Strings: A Primer
• Notes on higher-spin algebras: minimal representations and structure constants
• From Coxeter Higher-Spin Theories to Strings and Tensor Models
• Symmetries of supergravity backgrounds and supersymmetric field theory
• Higher-spin symmetry vs. boundary locality, and a rehabilitation of dS/CFT
• Mixed-symmetry fields in AdS(5), conformal fields, and AdS/CFT
• Cubic-interaction-induced deformations of higher-spin symmetries
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Solutions in Bosonic String Field Theory and Higher Spin Algebras in AdS
• Linearized Coxeter Higher-Spin Theories
• Stringy Symmetries and the Higher Spin Square
• The Higher Spin Rectangle
• Toward a Higher-Spin Dual of Interacting Field Theories
• Holomorphic primary fields in free CFT4 and Calabi-Yau orbifolds
• Two-twistor particle models and free massive higher spin fields
• New analytic solutions in String Field Theory: towards collective Higher Spin vacuum
• String Theory and Emergent AdS Geometry in Higher Spin Field Theories
• Scattering amplitudes as multi-particle higher-spin charges in the correspondence space
• Higher-Rank Fields and Currents
• Quantum Gravity models - brief conceptual summary
• Field Equations for the Simplest Multi-Particle Higher-Spin Systems
• Higher Spins as Rolling Tachyons in Open String Field Theory