Slightly Broken Higher Spin Symmetry: General Structure of Correlators

Abstract

We explore a class of CFT's with higher spin currents and charges. Away from the free or $N=\infty$ limit the non-conservation of currents is governed by operators built out of the currents themselves, which deforms the algebra of charges by, and together with, its action on the currents. This structure is encoded in a certain $A_{\infty }/L_{\infty }$-algebra. Under quite general assumptions we construct invariants of the deformed higher spin symmetry, which are candidate correlation functions. In particular, we show that there is a finite number of independent structures at the $n$-point level. The invariants are found to have a form reminiscent of a one-loop exact theory. In the case of Chern--Simons vector models the uniqueness of the invariants implies the three-dimensional bosonization duality in the large-$N$ limit.

21 pages + Appendices + Biblio=32; comments and refs added, matches the published version; ref added

References in corpus (10)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Light-Front Higher-Spin Theories in Flat Space
• Higher Spins in AdS and Twistorial Holography
• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• A Note on (Non)-Locality in Holographic Higher Spin Theories
• Relation between parity-even and parity-odd CFT correlation functions in three dimensions
• Higher Spin Gravities and Presymplectic AKSZ Models
• Four point functions in CFT's with slightly broken higher spin symmetry
• Anyonic correlation functions in Chern-Simons matter theories

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• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• Infinite distances in multicritical CFTs and higher-spin holography
• Basic curvature and the Atiyah cocycle in gauge theory
• On correlation functions as higher-spin invariants
• Deformation quantization of the simplest Poisson Orbifold
• Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes