The Higher Spin Rectangle

Abstract

The chiral algebra of the symmetric product orbifold of a single-boson CFT corresponds to a "higher spin square" algebra in the large $N$ limit. In this note, we show that a symmetrized collection of $N$ bosons defines a similar structure that we refer to as the higher spin rectangle algebra. We explore the relation of this algebra to the higher spin square algebra. The existence of such a truncated algebra hints at bulk theories interpolating between Vasiliev higher spin theory and string theory.

arXiv comment21 pages, 2 figures, Added clarifications, Version to appear in JHEP

References in corpus (34)

• W-symmetry in Conformal Field Theory
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• Counting Gauge Invariants: the Plethystic Program
• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• Symmetries of Holographic Minimal Models
• Triality in Minimal Model Holography
• W_{1+\infty} and W(gl_N) with central charge N
• Higher Spins & Strings
• Asymptotic W-symmetries in three-dimensional higher-spin gauge theories
• Partition Functions of Holographic Minimal Models
• W-symmetry, topological vertex and affine Yangian
• Coset Realization of Unifying W-Algebras
• String Theory as a Higher Spin Theory
• Minimal Model Holography for SO(2N)
• Representation Theory of The $W_{1+\infty }$ Algebra
• On the classification of quantum W-algebras
• The semiclassical limit of W_N CFTs and Vasiliev theory
• Higher spins on AdS${}_3$ from the worldsheet
• Stringy AdS3 from the Worldsheet
• Higher Spins and Yangian Symmetries
• Exploring ${\mathcal{W}}_{\infty }$ in the quadratic basis
• Yangian realisations from finite W algebras
• Even spin minimal model holography
• Unifying W-Algebras
• Multiparticle extension of the higher-spin algebra
• Perturbations of W(infinity) CFTs
• The Complete Spectrum of the $W_N$ String
• Fractional Superstrings with Space-Time Critical Dimensions Four and Six
• The $\mathcal{N}=1$ algebra ${\mathcal{W}}_{\infty }[\mu ]$ and its truncations
• Model-Building for Fractional Superstrings
• Even spin $\mathcal{N}=4$ holography

Cited by in corpus (3)

• Tensionless String Spectra on ${\mathrm{AdS}}_3$
• Instanton R-matrix and W-symmetry
• Symmetry Algebras of Stringy Cosets