Abstract
In the context of higher-spin holography, we compare the classification of cubic interaction vertices for higher-spin gravity theories in three dimensions to the possible three-point correlation functions of conserved higher-spin currents in two-dimensional conformal field theories. In both cases, the allowed structures are governed by triangle inequalities for the involved spins. It is established that higher-order correlators satisfy similar polygon inequalities and that the same inequalities are valid for higher-order continuations of cubic vertices in the three-dimensional higher-spin gravity.
Highlights
Higher-spin (HS) gravity theories [1,2,3] provide interesting extensions of gravity for which the holographic duality can in principle be studied perturbatively in contrast to the string theoretic anti–de Sitter (AdS)=conformal field theories (CFTs) duality
In the context of higher-spin holography, we compare the classification of cubic interaction vertices for higher-spin gravity theories in three dimensions to the possible three-point correlation functions of conserved higher-spin currents in two-dimensional conformal field theories
Higher-spin holography is to a large extent controlled by an enormous symmetry: the higher-spin gauge symmetry in the bulk, and the corresponding higher-spin global symmetry on the boundary [11]
Summary
Higher-spin (HS) gravity theories [1,2,3] (for reviews, see, e.g., Refs. [4,5,6,7,8,9]) provide interesting extensions of gravity for which the holographic duality can in principle be studied perturbatively in contrast to the string theoretic AdS=CFT duality. The main results of this paper are as follows: (1) In any W-algebra, there is a unique basis of quasiprimary fields for which the r-point correlators vanish unless the involved spins s1; ...; sr satisfy polygon inequalities: Xr si
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