Conformal Higher Spin Currents in Any Dimension and AdS/CFT Correspondence

TL;DR

The paper classifies the complete set of conserved conformal higher spin currents that can be built from massless scalar and spinor fields in any dimension, showing that these currents are organized by Lorentz two-row Young diagrams and by powers of $x^2$. It provides explicit constructions for arbitrary integer and half-integer spins, including a spin-3 example that illustrates the multiplicity arising from descendants and $x^2$-multiplication, with corresponding gamma-transversal tensor-spinor supercurrents. A key result is that conformal higher spin symmetry parameters in $d$ dimensions arise as the dimensional reduction of the usual AdS higher spin symmetry parameters in $d+1$ dimensions, supporting an extension of the AdS/CFT correspondence to higher spin algebras. This representation-theoretic reduction aligns the conformal and AdS higher spin structures and strengthens the higher spin holography framework.

Abstract

The full list of conserved conformal higher spin currents built from massless scalar and spinor fields is presented. It is shown that, analogously to the relationship between usual conformal and AdS symmetries, the set of the conformal higher spin symmetry parameters associated with the conformal conserved currents in d dimensions is in the one-to-one correspondence with the result of the dimensional reduction of the usual (i.e., non-conformal) higher spin symmetry parameters in d+1 dimensions.