<i>S</i> = 1 in free <i>O</i> ( <i>N</i> ) vector model/HS duality

Abstract

Following the work of Maldacena and Zhiboedov, we study the implementation of the Coleman–Mandula theorem in the free O(N)/higher spin correspondence. In the bi-local framework we first define an S-matrix for scattering of collective dipoles. Its evaluation in the case of free UV fixed point theory leads to the result S = 1 stated in the title. We also present an appropriate field transformation that is seen to transform away all the nonlinear 1/N interactions of this theory. A change of boundary conditions and/or external potentials results in a nontrivial theory.