S=1 in O(N)/HS duality

TL;DR

This paper investigates the free O(N)/Higher Spin duality, demonstrating that the S-matrix is trivial (S=1) in the free UV fixed point, and explores how boundary conditions affect scattering interactions.

Contribution

It provides a bi-local framework to define and evaluate the S-matrix in the free O(N)/Higher Spin duality, showing the triviality of scattering and how to remove interactions via field transformations.

Findings

S-matrix for free UV fixed point is trivial (S=1)

Field transformations can eliminate non-linear 1/N interactions

Changing boundary conditions yields a nontrivial S-matrix

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 non-linear 1/N interactions of this theory. A change of boundary conditions and/or external potentials results in a nontrivial S-matrix.