On Higher Spin Gauge Theory and the Critical O(N) Model

TL;DR

This paper demonstrates that the duality between higher spin gauge theory in AdS4 and the critical O(N) model in three dimensions is precisely explained by boundary condition changes, confirming the conjectured duality order by order in 1/N.

Contribution

It establishes a detailed correspondence between correlator differences and boundary conditions, confirming the duality between Vasiliev's theory and the critical O(N) model.

Findings

Correlator differences are explained by boundary condition changes.

The duality is confirmed order by order in 1/N.

The critical O(N) model is dual to Vasiliev's higher spin theory.

Abstract

We show that the differences between correlators of the critical O(N) vector model in three dimensions and those of the free theory are precisely accounted for by the change of boundary condition on the bulk scalar of the dual higher spin gauge theory in AdS4. Thus, the conjectured duality between Vasiliev's theory and the critical O(N) model follows, order by order in 1/N, from the duality with free field theory on the boundary.