From Coxeter Higher-Spin Theories to Strings and Tensor Models

Abstract

A new class of higher-spin gauge theories associated with various Coxeter groups is proposed. The emphasize is on the $B_p$--models. The cases of $B_1$ and its infinite graded-symmetric product $sym(\times B_1{)}^{\infty }$ correspond to the usual higher-spin theory and its multi-particle extension, respectively. The multi-particle $B_2$--higher-spin theory is conjectured to be associated with String Theory. $B_p$--higher-spin models with $p>2$ are anticipated to be dual to the rank-$p$ boundary tensor sigma-models. $B_p$ higher-spin models with $p\ge 2$ possess two coupling constants responsible for higher-spin interactions in $AdS$ background and stringy/tensor effects, respectively. The brane-like idempotent extension of the Coxeter higher-spin theory is proposed allowing to unify in the same model the fields supported by space-times of different dimensions. Consistency of the holographic interpretation of the boundary matrix-like model in the $B_2$-higher-spin model is shown to demand $N\ge 4$ SUSY, suggesting duality with the $N=4$ SYM upon spontaneous breaking of higher-spin symmetries. The proposed models are shown to admit unitary truncations.

50 pages, no figures; V2: Clarifications, references and acknowledgments added, typos corrected V3: minor corrections to match the published version

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• Towards higher-spin AdS${}_2$/CFT${}_1$ holography
• BRST-BFV and BRST-BV Descriptions for Bosonic Fields with Continuous Spin on $R^{1,d-1}$
• Planar solutions of higher-spin theory I: free field level
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• Rectangular W-algebras of types $so(M)$ and $sp(2M)$ and dual coset CFTs
• Higher spin fluctuations on spinless 4D BTZ black hole
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• Holography for Tensor models
• Linearized Coxeter Higher-Spin Theories
• On the spectrum-generating superalgebras of the deformed one-dimensional quantum oscillators
• On tensionless string field theory in AdS${}_3$
• Scattering amplitudes as multi-particle higher-spin charges in the correspondence space
• Topological Fields in $4d$ Higher Spin Theory